HYDRAULICS BRANCH OFFICIAL FILE COPY

' . ··- --- 0� 0 ------REF·ERENOE -.0 t-- r-f r-f NOT TO II; TAKEN fRO_f\4 THIS ROOM Unit�_ ��-- Depar11ae11t of tlw. l111erier , .. • ; ,.)114 · �------Burea• .of Reelamatloa ,.· '

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( u.s.B.R. Translation - 169: ( F.xperimental study of the expanned hydraulic jl,UDp ( (Experimentalni studie vodniho skoku vzduteho), by Jan ( Smetana. Zpravy verejne sluzby technickl, 1934. Translated ( from the Czech in 1942, by Kalal 'Hydraulic ( Laboratory ( tr.s.B.R. Translation - 170: Report-106 ( Two instances where the rational theory of below dam ( sections was used, by Jan Smetana. Reprints from national periodicals, ( reports of regular technical duties, 1935. Translated from the ( Czech by A. D. Kalal, 1937

I "".. • . �) ! . � .�·

Traneladon No.169 $." 170 ...l· ,; 1937 and 19li2 r.

TABLE OP -GONTENT8 -- Pap:o two .'t '?ABLE OF C ONTENTS

8 l8.Bmp1r1cal Formula ror Dlstanoea 1 rro� t�o Gato to tho A.LI�ITING OF THE TERII.Pt..AN AND CLASSIFICAT70N OF T�P. TESTS. Least Depth h • 4 l.Ltmtttng er the term

l9.Emo1r1cal Formula ror Comoutlnp: the Least Depth h4 • ::>.Prov l oue work

E.DBX::RF.ASE OP MECHANICAL ENERGY BY SWOLLEN AND UNSl'fOLU:N HYDRAULIC �.Arrangement of Teet �outoment

\I JUIIP () 4.Resolutt on or Teets 20.Deorease or llechanlt.al Eneriry Resolved for None1arttc Watter B. SOL''l .0 OF HYDRAULIC JUMP

21.Decrease or Mechanlcel Enerp;y or Platn Hydr11ultc Jumo 5,lleasured Values ?2.The decrease or 11eoh11nlca1 Enenry or i'l.Ptn �ydraultc Jump 6, C .,mputatt on or Throup;h �'l:>1" t t of Nater ·,,htrloo.Jl 3 4 Exoreeeed tn � or 11eohanlcal Enerp:y Hr 1n Proftle I 7.�esolutton of Water Whtrle Above Stream Proper

23.Decreae& or llechantcal Enerp:y or Swollen Hydraultc Jump 8.Ho�tzontal ?lanes of Water 'Rhtrl

24 • .rhe decrease o:!' :Jechanlcal Enerp:y or SwnHen �ydr11ultc Jump �.Prebsures on Bottom r Resolved ln-f. of- llechar..tcal •!Mrpy P.� tn P orne I c� 10.toectrtc We1Fht

Plaln Hydraultc Jumo 11. Pressure Hetpht and Coefflctent of Out flow for flatn and

F,Su"4ilARY OF INVZf'T:GATlONS Swollen 1�ydrau11c Jumo

12, Hydraultc Reac ton tn Unconfined Proflld

13.i-lydrodynamtc Eouat1·,n or !he Water Body or bNollen Hydraulic

Jumo Between Profile I ana II,and Comouta ton of Cepth h 3 or Water Rrh1nd GAte

J 14.HJdrodyna�tc �c�atton fhe na or Dody Between Proftle I'and

II(Ftp.3);Comoutatlon of the S�alloe Deo�h h4• D.LE:iGTH A!'l:, �;_,op;;; OF T_o,> O? ·•;oLL;. HYIJ..U.'JLIC JUi.'.?

15.Length 1 ° of Swollen Hydraultc Jump

lo.Slno-, of Too or Swollun Jump

!7.2:nolrtcal Formula for Comoute !"Jn of the Dep'h of ,Ve•,!!r r. 3 Beh1:1d he Gate ,_ ... . -- ¼- -

a 3 overflo• and called thie •wasserwa1ze• but m i nly etud1ed the s1ze of· lenFth and mm in diameter from which were led rubber tubee to euepended ... t,(o# •� ti P graduated glaee tubes opened at the too. water rolle and thetr ab111ty to� mechanical energy. ietr�weky a hydraulic 4. Resolution or Teets accomol1ehed 1n the Berlin b•11ldinp:,eever l tests wtth ewo11on hie tests So that we might analyse the swollen hydraulic jump on all eidee , ju:np along with plain hydraulic .lump.He states himself that a very and so we may show its organic connection wi�h plain hydraulic jump(or have rather· a qualitative value because ·1hey w re ccomplished in n or be1np: measured. which are stated poeeib1litieC in balance of mechanical energy)we resolve small troughs and some ouantities were comouted i stead a a by measurement of tests thusly: Several tests of th1s nature were a1eo made by Woycick1 in ·the l bor tory ,J ,/ J._, ',;N We O'lBn the gate to the heiFht h2 • 0.04m (Fig.8) and g1ve under _,curychu. dt'd ( its sharp wall a� q c O.OB66m3/s(For' lm width of trough).Before the Written d1scussions durtnp: the last two years 1n the oertodical

,..)__ a gate occurs a water surface of a he1p,ht h1 :0.666m,and behind the p:ate Lie '.Yaseerwtrtschaft of ll'asserl{raft nd Wasserw1r!,_s9.haft (Koieny ,Safranez, the torrential current would .have the least depth of y � 0.0255m and vel- Lud1n) .have for their theme pla1n hydraulic .i umo and the change of enerp-y of e oc1ty V1 = ; = 3.394m/e,thus the symbol : th water rollers.These oaragra;,hs however do not cover fo�ther'�este 1 ', w1 � 6.79. ( Srovney nor do not state def1n1tely the testsconducted by these authors. explained th1s test in Study Al.The deoth .of the torrential stre9-n rises � 1 � &afranez does not consider h1s tests on the swollen hydraul tc as •tL loses soeed and th1s increase 1n he1plrt-meaeurss 2.5mm,ror the f1ret Jumo ae comoleted, �or 1nstance the comoutet1on or the length of swollen meter or length or the trough. IVhereas be1p t Llt 1s resist 1ne- he111ht, hydr•u•tc Jumo(Le1der 11epen h1erfur, sowett uns betonnt 1at,so gut w1e expressed, '! p:ar 1':e1ne Versuche vor) .5tra1phtwey Kozeny states there 1e a lack of de­ finite tests on the subject. and symbol can be fixed from th1s equation. a 0 3. hrr ngement of Test Equipment. We take a known t nstance of ;:>la1n hydr u11c .,u-n;, where tt crosses ------, I have conducted tees of swollen hydraulic jump 1n that teet1np: a torrential stream :if a depth y 2 = 0.2305m (F1F.B) and 80 velocity troup,h where for'!ler est.a of olatn hydraulic .lumo were made.Arranp-ement v 2 ; 0.3756m/s. The he_ip,ht of the hydraulic Jumo s r r = 2 = ts : Y2 - Y l o �sta(F1p:.16)shown 1n Study A,were mod1 1ed for the new tests s that

= 0. 205m and the lenp:th 1s 1 = a 0 e cotF. (y? - Y 1) 1.16m, where cotg. a • 6 measur'!lent of actual pressur on the bottom of • he troup-h could be made. ( v1-z. Study A, Parapra ph 11) To p:a1n Thts end,holee were bored tn the me al bottom of the trouph and In Study A, 1n parae-raohs 7 and. B,of hydrodynamic tnstances, r nineteen holes were olaced on one half the width of the trouph.Ooentng have shown that the accqu1red 1nformat1on from thts one test makes 1t No.l (F1p:.8) waslatd wtth 1te center on •he lowe edp:e of the metal p:ate ,

e ooestbleto exte-oolate for any measured tnetance A 1 eo lonp: ae the char- opentng No.2 was olac d a dtstanceof 5cm below o.l and opentnp: No.3 was

acter of the test of a F1ven symbol M1 = rematne unchan,ed.So ouan- 10cm -�rom ooen1ne- No.l,end he others were soaced 1n rn·,1t101ee of 10cm dtstance�.In theee holes were carefully soldered coooer tubee,Scm in t1ties v1,Y1 and q etc, -nay assume vartous absolute values so long as -,. �'- ._,.; � 'X ,: 1, .J� -� -a:· !"" � -,� r 1Vely name "solitary wave" :"'l-(e r\ a r� "sol \ t A ry •�·,e" le altogether dlff- l .Ll11tt ' nil' o f ti,,. ter'II . erent from t he na'lle " oclllatlnl' w"'ve" . !n the forme r a "<>� ttlve soeed \ly ------•� . I ' .. ('.," --- - - �-- The Exo<'rt'll& ntal St udy of Ju11:> 1s B C'lnf. 1n�·� 'Oro 91,rr·ted U1reul'fl ftow t s obta tned ;tn the lat ter no �.)+->, rf- 1c ob- Swollen Hydrl'l'Jl • c Rt ton of m:, wor1t Exoerl:uent.al �c!l'. of H;ydra\al.1� ( Re oort s of Re �ul li r talned ,but. there 1B on ooc1llat lnl" chAnFe 1 n 'h7m ln "lite t'1at a torrent ial etre'l.m of n Flven ne,.at lve(water surface 1E lowertnF) orogree atve( oroFrec-sln v uo stream or the symbol of torrentne&s � and a F1ven deoth ( F1p-.l) croeeee tn rtvor n l y1 d owns tre a-n with oro,rre �slnF eoeed ,na 1 tr. �nlr.f' d:,namlc orullltbrtum) . or the etrea11 of' a deoth y2 by a hydraull c .1 ura;> of httl Fht. s • Y?.-Yl s t atl oar:,(unchanp-lnl" lts oos t tt, n ) .Hyd !"s ul tc ., u:no,olatr. and �•ollun , le Le ' s ta"1-e for e 1a'11ole t"'at ..... 'h" •est wh\ch I h� .. e covered t'iena for11 or' oos ttve' and 'etat lon ary ' solitary wave. tn Study A, Para,:re o"1 4 ,wh1ch exolatns the •est la1d l n the fart.her end . There fore t>1•t preclee n111 -ne "iwo1 1en hydr>11J l le .• um-," wa,· ter'!!� A n r." of' testlnF trouFh wlth a checlt £F&te we r!! lee t h-• dnot"1of t"1o rtv�r etrea,i by Koc!-. "Wasserschwall�by Rc h'b ocl{ anc!Bos P "Weche 1e-,r•mp-". /1 , •'1t ° Y2 • o the de 'lt'iY 2 by 'lf'11ch that. only ln •he last oertod dld Pletr :iws',y uee th" nn �." "u1'eret8ut E-r 0 Y Wassers orunfl'" . ? " OY2 ( 1 ) n here �ln 1n ht, o•.vn teats. on ova��al l s m c!e ucc of the term, w D could bee.valued as o • 1 to · •• Enl BrFtnF Y-;, on y,;,':, , t"te ola\n

"naooe a reesaut elo1Fne" �o d•.rncrlhe the ohenomena '>l r.1.n hyd rau1 lc ju'l!o or s111-,1� '1ydraul1c .1 u·nQ ::i·>'tee ln kno,m 11111tr uoetream unt l l lt leans

and "na ooe 1.nfluenc le por laval" to deecrl�e wh8t · le •h,uFht of t n thls atralnet the FRt'l ·and oa1Jses \n •he orooer :nant fe et.atl:in w'ilc., ! ::!eFlr"

s tudy as swollen hydraulic jumo. 5 'o name ' Sw ollen 'iydraul le Ju'l!p' or 1n ahort ' o•, e rfall ' ,wiieras oro-

trree e tng hyd raulic �U'DQ ha e the onerpy neceseary ro turn lt eel f ,o ve r

Ng_t..L2_ Mr. Dannell ,dlrector of •eettni:- lalnrat ory of Neyret­ and thte t urntnp over occ·1rs by the gat e,whore fro11 lt t e obt9 \ n od !he ;, Beyll ter 1n Grenoble p-a•,e 11e the French Ft.ate'!le n t "reseaut.�:-� well l{nown ro• ,.tton of' wnter 111r-1und the liortzont!l l ax is at-ewe th-, ntrea,n

and I bel ieve there f·ore t'iat. title os rt lcular 'lheno,ien a har net Ol'U'Dlln" , Ot'ie rwt�e lt 'Dl Fht be oo r r,t�le to uee t'1• ter,ne ' 01noed 'iy� -eul lc .1 u11"' or ' been es oeclally etud led by the French,and tha t theee terms are RR \ee1 'iycre,11 le Ju-no' .

used thus for the flret tlme. Thus the d"Gt \ nee e NOl 1 en '1ydrnu1 le .• umo le measure,, "or de ot h a nd l enFth or et \l' lnf' 0001 as I li'l ve elio-.vn t n •he art icle Below_,,,.t,-e 2. �.!!.!.�� �_!!ter_�tl! :YQ l�-�� -�l!!r_�!!�t� �Y Hus t nec .(Reoort� or �eFul�r Tech­ n t ca 1 Duties From named aut hors decend al eo tes ts of t'1l11 s a:ur, ohenomena . , 19'111).It ls desired t hen w1th thlB evidence a t hand ,to ta'fe 8n interest 1; a c11re !\a l •vay n �arms tadt labora tory accomol lehed eevaral ,.,sts 1n whlch t, the PodB of tectln1cal pi-settee. Koch lnI the 1 a curved ,Reh The plain hydrau le .• u11p and also ·�P swollen hyd r,.u l \c jumo t,�;0��1;'°',i·� q fl '>wed out beneath t.he ,rate of wall boclt ln elo c Karlsruhe , observed 1n minute detail the rotation or wator by outflow a nd b n,r ln the c11tairory or hydrodynamic ohenomena whlch we c "n co l l e t- .· ..� -, 'i:,; • .,

1.. ; , __ they rema\n 1n the -neee ure of •he Fiven iymbolc Y .so the w -,le catep;ory For h1Fher va l ued than 10 . 8QQ of ·�e symbol •1 and the t� 1 h A \/ o f -nantfestat \-,ns o� e1m1la r character ts �1ven a value t he ol a1n unamec now q = o.oasta,;s these tes t1n,r arrenFement dt-n·ns 1ons are \neuff1ctent I . --' ym = . 0'5 llm'.'l /a for m widt of s bol 1141 .To correct a f1JC\np of 11&n\ f'P.r-tat1one of fixed oro oorttons , t here fore we t a're a sma ller t�Peupl 1n a coopernt1ve acsoc 1ated Mi and vary \ntr o , t'ie rest of t)ie o roi:>oeed. test rows wlll t-e :model for ola tn hydrAul tc .,U!D? O" 1 and swollen hydraul tc ju-no o -:-1and F&lned by sel ecttnp otl'!erM 1 • The other •i 1s FB1n�d by the t��lft show the orirantc stnirul ar nature of unswollen and swollen hydrA u1 1c ju-no o = O.OM66m'5 's by chanir,.nl!' t he o pen1nF of t he gate h and their ener�ettc ba ance.Symbol 111 was used f'or �he first t\!118 I 2 .we wi 11 tal

i.e. we are showlnp. the resul t of IIC tests carrte-1 out. for ola\n hydraul ic teats for a consta nt Mi = 6. "fQ , b ut for vary 1nF val ues of symbol l. , udy A,row I and Jump(Stl,ldy A,Table 1) �lain hydraulic jump,wh tch are 1nd1cated 1n Table l,St

- .- .,. ,."1.·.,. . ,r ,. ,. -,,. i, 8 / ' ,_,,. t;. These teats whtch J w111 an al7se tn later et�tements ,th•se te:t'O No .1-6 and which weroirrouoed by 1ncreaeee 1n the linear 'l!easures of the are organic and eyetemat1cally to the ourooee ,and have preat�r scope dyna'111C form ,I a l,2,,,4,6,1;,10, and I ch&n'7ed for s,ollen hyd raulic jump than practice can ut111ze. values p • 1.1 to 1.6,reeo.2.0 anc 2.5.By th1s was iratned mater1al for six further rows for the ftret le�1slat ion of the law for forms tn the B, SOLVING 011' ' HYDRAULIC JUMP· reeolvinF = 1 to 10 . For the ltmited reeolvtng of thts study ,I will

5.�eaeured Values ma1 and a �ate opening of s f' (Tabl e 1,Column 15,4) .All depen�1np quantities were correctly measured Coe�fictent of,;rl �·· under pata µ t •he prod,ict o the coefftctent h2 s o f v�loctty , (lose) and coefficient of contraction .Loss coefficient ,the1r value for hydraulic, jump1 unswollen, t.e. for o:;1, were moat .• 11ccord1ne: to Lesbroe e � <>ra1101,11·•a o_q9 •o o.q7 for emAll to conercl.- generally taken from Study A. 1�. ,.pati'.u A$-� .

0 t Note: All meaeurmente were · made the same as ror Study A,by Coe ff1c1ent for out flow under a sh r� Nall and o herwtee for �r.L. L1e1

Romov for h1s ass 1stance tn obtaininp literature . Thte then 1nd1cates tha· the value ts a lt11tt from �htch on b,th el�dE ero,,e .

We :neas ured : Coefftclent of contract �:in oJ' •orrent tal rao--e'!.e11t ) .. t-, \nd a) With a P91nted measure,the he1P'ht of water plane be fore pete ln our case t£ ° the �ate h1 (Fi11.2), the he tpht of water ol �ne behtnd •he uete h3 ,the lowes t ordtnates of surface h4 , the he111ht of the water olane after the �e,• ort11·n·l Pa 11e 10 hydraul 1c jumo y2P ,(Table l,Column �.6,8,5) .�or rows VII we measured ( 2) 1n deta1l the entire surface. b) Wtth a len11th ·easure ,the ent ire lenpth of swollen hy ­ that •>-,e 11111• u - 1 lndtcet" 1P,!.. e. the hor1zantal distance of thg oro ftle II fro 11 :he �:e can th n e·•:>ec 1 .9 w11l 1·e 1 s tn a r1xed manner even tn awe wh\ck we derive . The Hma11est value of the P"ate(F1g.2) ;also l ,i.e. the d1stunce af the smallest ord lnate h4 from the gate 1nd1cat1np the distance of proftle r l from '.he 11a�e , the length ey11bol i.'.1 = 1.641 10 1'1cr1 i.t1!lr. 11 tc 1·.,, tt . . ..._.

j 1 ·\" ·, ,,,,. .... ,:

O O a r l r CO':!Olet tnF. l , thus l = l .. l (T�":-1 ?. l ,-:o�:.nn 1,l'.l) . as ls shown by the curve -14 ln'Ftg.9. c ) 'lltt'i J::'"l!'l end ot'lZo tnts ,however only on teete c to we obtatn the produ t of through fl ow a a 1 3.Of t 'I we �now only tha t tn pro ftles I a nd II that 1 '1 a O.The oresum ot ton t ha• 1 3 � t 4 tn t hese d) �tth a 2ttor ·�ho we -nea�urec •he veloc tty or the water c ross nr oflles does not need • o be ful ftlled . Rut. as can be se•1n tn '!'abl e 11 !ll 1111 1 !'1 f1·1e eras!: P!":> 4" 1lee 1 1 ,r ,1 , 1 and I:( F 1J7 . ?) . Pro"!'1le 11 i"i'a8 2 ,when we ore ;,are t'ie dtfference ,q = 13 - t 4 ,w" obt!ltn ai.moe t o!'"ectsely latd at the oOt!'lt o '" lowe,:t curfrice,•hus at the distance 1s fro r, ·he a . Th is ,s evidence that the oreeumo• ton 13 " 1. 4 • 1 t r. well satt �rted. ..-ate. The oth�re

quant lt1es See copy Paee 12 The prent o•.1lsR• ty1 n_.qrer , ..,· ., �-�t e 'Jr?r-iL<.. ht t,�d ,:9.:-..-. �ul -ne9. :-:11r·�11ent, there . c From i:ierformed -neaeurements of throuF'i fl ow 1 we an conclude 0 Ftir.O tnt rod11c"S a , ..·1 t"ri••· •• tc c,1t -nad•• P.J c �r• -- _, r, J.• l hy , .v ·neae1..1red �estF that ; fro-n rJW JII,� = 6 1 . 70 "•n .: 0 = l . ?; tn whtc>i ar<> eect t:ins c1•,1a,,d by = :. 1 a)That. wlth Freat or'.>Jl:e'l!tty 1 '1 1 4 'IBloct• teP , b•1• only tr. cu: oenB tJn "ll ac ,�u tn .,..·,� ax�� )� ·�e ·es!t�� tr�u�h oro f1le ity that chAnFeB from proftle to b) 1 ts a quant 1 F1p. l) !'lt rodc1ce,, ftve v<>loctty 8'JP ')f!n,•ton11 ,a" q cr-:>re "Jr'.l f t le 1 1 -ns:!e of s wollen P and w 1 th e y'llbol M c ) Increasee with the measure fro� ·h�ee tee•g l e not s tat lonary d )MovtnF resultant of hyd rAu'. tc ,lump . -:i o t 6 C�_ �_t_:'-_:_ �:1__ 0 _:_ Thr_.?_� J_l_o__w _t -'-'..._ ..t ,. ? f.... 71_ __Ater_ __ 11"11rlo:l )l . 7 . Resolutton of Wat_e1:_ Whirls Above �!,rea;n Pr;i,:,er We can ee0 �ro,n thA velocity 1ndtcat t'.lns(F 1iro .a Rnd l)) t'iat tho We c an take the examol e of the water wh1rl abov� the ma in stream 1 ..- reat �st velocttt e e are n e 9r th" b ottol or tho teot1!'1F trouirh.Thee e vel- ae a tumlnp water body , that ts lald down tn Freater conn�cted bel te ,as -:>ct ttee measured tn a dtrec tt ,n f ro-n 'he �a•e decreaee ae ·he het�ht tn- le shown llluetrated 1n Flg. 3 .Croes cute at the center of the body 1nt­ crea ee� and travel toFether to 6 , a nd in ooelt tonP a�ove o chanFe t he t r ereect more water belts than on lte edFee . d1recttonc 'l nd 110·10 toward t h But thte wh1rl 1np movement ts marred by a .eotral movement ,ae If we ·CO'l!Oute the �now!'l Fr" phtc11. 1 tnteperatt on t,i • ndtv tdual le shown tn Flg.9, whtch the eye of the observer c i,n eee when ecout tnF oroftlee , the hlpher ne1 ira •_t ve onrte :>'.° eus oo nd ed veloc t ty t nd1cR• �,we a ter trl ts broken the whirling o! alr bubblee.Beetdee , the too of •he w wh obt 11.tn t.lu ,,,1..-h q:,w t4, whtch 'IIOVee on t :,o 1n the dtrect 'on •oward the enFth wlth tncreastnF by a wh1rl ln$." out flowlnF cone wh1c"' tnc reaeee ln etr iral e.Valuee o ! tlirouph flow 14 are ln T!lble .l le made a ·,ery '.' . In orof1lee I !l nd II, I'l ,and with leeeentng P.Namely ln port tons of too f,F, 1 l 4 = O .Through flow t 4 t e chAnFeable , and hc r RnFee ror.i or oftle t o oro ftle dee o c one , whlch breaks the olane and leads atr 1ns1de and adds to watnr n .. . , .._, preeeure 1• ooaparebl• to increued hei,bte or the free top eurface, and bodies f,F,J,b,f, such 1mPU1Bee that \t actually turns about suspended // t.he pressure on the bottom 1e comoareble to the he1p:ht of a column of axis. water. 8.Hor1�ontal Planes of Water Whirl

Let the specific weight of water in the mninetreea be y1 and 1n Scouting theoretically turning a�ou• or water tn water whirls , the lower port ion of the water wh;tl be y'3 and in he uooer port ion • we oo1nt out a material pn.rticle m(Fiir .4) .on 1t ra 11s the increased lfeiFht y4 � -r fuFal force rn2 Then manifests 1teel f 1n the-p1ezometer tube the hydrostatic ores eure g . and alsor centri - p which ta circum'erentlal �.Both ..._ 1 on the bottom or I , + f _ "t < increased speeds may be determined for the symbol !!_;,, which ,ee deter:,nine y '1 ; b)From curves of water f1bere oriFinete denentertnF pres•- �ra ,h lcally wlth t'1e C�rnot equat1on. Hor1zontal pl aneA are peroendicular uree and so: to the dlrec•1o n g ,v and le a rol llncr olane coveratl partly by r from ootnt I o l Pressure z1 formed _}by "', cu rved"I rtb ere of the maine ream.Curve of . Point o ctianges ooe ltion by " change of a ra llroad curve turn1nF fiber of the mainstreamls large between the share wall or the gate and about oart 1cle m,but remein\nµ always above too of the smoot'1 surface. or There fore all 1e·,e1 planes are concave to the ooint o orofile I) ind lcatee the contraction t'1e ray .Comparitive oreeeure is The tior1zon al Dl"ne ts oleo t'1e too aurface whe::-e ore ssure • manifested in known values z1 in piezometer tubes No .l and 2.E:xor�Aely 1 I remark ,that profile I le situated close be'1ind the r. ontract\on;there fore �easured wit'1 an ooen b1ezo�eter equals z�ro . The top surface• ts also a 1 for rro file I, z, • o. coverinF olane for roll r olenee dee tpnated from various ol " cee o .Ord rl y The curve of fibers or ma tns tream tn its furt her oroFress beyond and quiet sw trl1np ta ob A1ned at all '1\�her values of p,For theee tns tancee oolnt b , by ex olanat ton of pressure z t'1ere should not be any oress­ 1s shown t'1e whole to:> as a concave fo rm. This is a ne·R lnterestinp con­ 0 ures . The cotton threads ,fastened on susoended rod s show at the bottom c luston ful ly And oro oerly obtatned by the form or aha� of the 11ne de­ in a11 pro files a horizontal situatton (Fig.5,6,7).With great �earnese D1cttnp the oo surface 1n Ftps .8.7,6,5.Flps 5,6,7, aM ohoto�ra?hB of

we can conclude that the ore eeure z1 = O,between oroftlee I end II. swollen hydrsul �c Ju�p of the same st�n � l = 6.79,b t various measures -;>re-s suree ·z from the curves of fibers of lower be lts of the o f swol len pc1. 2,1.4,1 .6.- 3 water whirl ls vary1n!!.It ts greatest wher ts ·he Freetest curve of fibers 9.Pressures on Bottom so et th e bepinntns acc1dently at the end of the water wh1rl .Th 1s prttesure Acco'lloany t np hydraul ic 1:.i;n:> ·he fo llowtne pre !'curee on the is oulsat tnply increased by a slant inF compl icated oressure oripina \nF from decreased solral movements . a)In •i,e 11a 1n st ream occu::- oart\cles of water,mo·,tn� wtth .Pressu� z from c:.i::-ves :if water rtbers in htp-'1er bPltB or ,..ater e:re'l er oeed \n · i,e lane of he uaed oroftle. 1 !> Ae due to the height of a wat .,. �r:,lt.n.r, of e pea � fie we1Fh 'f -: 1. he ore�eure 1n 11au1ds ts equal 1n al l d1rect1ons , therefore '.he I '

:.;� the'.'1 +r.e ·1:"n �e o t e z ometer h«hFht t• �tat\c P (F1F. ")

"3 (3) values r' tn Kp:/dm eoual 1n dtetanc ee creater fhAn Ordinat-- l tnee o!" -nec'ilntcal en"rl"y te irtven t'.i:i •he eum of etat1c o.66R ,o.g00 ,o. 9'.JO .

7g 0 4 For swollen hydraul \c .,ump tn row ''rI,ii!1 = 6 . , f' 1. , was tn�en and z was co�c½" ocl from eouat 1on 3c.Values z 1n 7atle 3 :arrl ed (4) are values o f Corlte ' n·1mber,t··· tr ac•ual values we co'.lnted far the fr:nn uro f\les I 1 to I 1 '" Thetr etze decreneee��h� d!rect '.Jn of t he �a1n stream. If we hold the eame s1ze z even for !he 1 ne t ance when � = 1. 2, mA ln e�rea� fo r oro f tles r' to r·' .The tr values are tn Table ? . The then we comoute fr,rn ecuAt1on "3a,values values collect tvely are trl �l ine ,and may be aeeumecl as a=1 .

('Id) 3 1 which are carried 1n Table 2.The leaet .. 0. 8') Kg/clm for oroftle 1 . 7he soectftc wetl"'it of watPr 1n �he ma 1nst rea-n we may asEume Of eoeciftc we1p:ht of water tn a water w1-.1r1 ·,, ., '.!l�Y •h e n c·Jncl ude a lway s BE y = l . Atr bub�1 es wtll enter even the ma tn etream, bu� only on

11 1t 16 S a)It decreases as p Increase" for value£ '.J - 1. a ::,,Jl e<1t tn1" occaston. pe ctftc wet,,.ht Y ,y 3 4 are actuall y EO'lleWh!!.t varted ooes 1�le to aEeume . I "t-'.1• tt ts not ea'3�ly eo determlned .Therefore we f'urther A1-..aye state

b) It clec reaeee ae u1 Increase� . Y 3 a y4.,h�n equatton ( �) chanpee form: c)Ie lesser as The oro flle IE nearPr •o th� v�te hetwoPn ( 3 a) � '1rofile s I I I . In eauat ton 3 a are t.vo UP'<:n,,wns :.7 4 11 nd z. Previousl y int roduced authors r,tatec.l ln their co,i:out�t lons •hat aeeumtnp that z � O . T'ien we calculate from �a.

( 3b ) 11. l'reesure Help-ht encl Coefficient o" Out f10>1 for 1 ------Specific weicht '- ;; ts l"reater than actual . f:,r 1t includes S ?l ain and wollen Hydraul i�-��mp. also neFlected pressure z.Thue we comoute for profile I. If -.·e increase orop:reee1ve�y the ov,tn hyclracJ1 1c .i umo the hei17ht Wtt'h hiirhe r vnlues of p,fro'll p "1. 4 , we may .1 udp:e by 'llany s mall of the water surfa ce increases 1r. front of the p:ate h1 P, as ts p:ra oh1cally atr bubbl es ln the water whirl ( F1p:.6) that :then we may , for and numerically illustrated in FiF. 5 . Its p-row th h '1 H, eoual correctly 1 these tnetqncee compute from "3a. to the nuant lty , whtch ts s ymb olized tn F1F.2 2. · I ·• ( 3c )

CO!llPUt 1nF the soecif1c W81Fht from eouation 3b for p latn ( 5) hydraul ic Ju:np fro!ll rows VII (J111 = 6.·,q,o = l l , t he 1 tr values are by To "h1s :: e brini:r r:at,1 in FiF. 8 , that 1B aoou rt enant values all !lleaeured olezometer he ip:hte P and meas ured too 1 e·rn11, abov(> �ottom 1n obtained 1n tests . There ta then the same difference between the water pro flle p1ezom�ters "3 to 13(F1,- .8)there in Kp:/dm� :0.31"3 , 0.414 , 0.534 , 1. evele on both tildes of the 17ate for both 01a1n nnd swollen hydraul ic Jumo. 0, 638 ,0. 701 ,0.75 2 ,0. 809 ,o. 823 ,o. 3·.30,o . �82 , 0.900. - ., •.. - --

I(.

Values tn eq�at ton 5 are pro oerly aool 1cabl� 1n both mant feetatlons.ThlB adde further welF,ht to a s1n�l e ener�et1c instance and interest . C,COUPUTATIONS OF HYDRODYNAMIC EQUATIONS BY IMPULSES Woyc lck1 2 ) 1ndtcatee tl'lat 1t 1B pro oer to take the dtf'ference of press­

12.Hydraul1c Reactton 1n Unconfined Profile ures of he1pht h1 - h4 . He sldeeteoe the erroneous tnstance that y tn 1 A sentence g1v1ng a defin1t1on of tmpulse,also tts use for profile I has the least value, hat ts Y1 ,atates that lowest oo tnt of forming hydrodynamic equations for water bodies between oroftles I,II, surface level f la above smallest y.D1etance 1 5 the m of platn hydraul ic jump I have given in subcha.ot,e.r 5 1n Study .There I from the pate ts always not iceably �rester han the distance e "hP. least 7 A t

and com:JArtt1ve veloctttes v, \.1 , \ 'f. 1n eauatlon 23 and ?4 . 1 It ts 'hen a hydraulic reaction R tn unconfined oroftle 7. The coefftclent of out f'o� for ola n nd swollen hyd raulic ju�o Eo1211t.iefl R = T � J See copy Pape 10 (7) le obtained frJm oractlcally the Sa'lle value. To 1ndtvtduRl' 1m:JUlses we i,lve the symbol a,so hat \\' 8 mtirh The coefflcten o" c,,n ract t ·,n s obta nee "ro'II the ?rooor- obtain an apreement tn the exoress1on , tton of oreceure he tpht o helpht of 0·1tflow •) 0utf'\. ow �nt? •esttr,i, tr?uP'h and for outflow •md er from curves of fibers z =-oand count the s ubstitut.e.d that the whole ?re�:cure � s pec1r1c we11tht 4 Oy e .- ua ton 'lb.w e ob- curface ,tt ts ) be exoec ed tha ,reesure he �pht was ta�en tnc?rrectly 11 '/ .• .,

t l. curv 1 R/ "' R11 we ma intain 1Jre a lso in a vree-nent wi h/' .,.reeolved �:,· the tatr. thie value , ,= By e 4 t n FtF.� tn oro �tle I �md II 91 1 3 .. quadrat ic equat lon : 1 4 : o. /' l L., + n 'I Impul ses turn1np £UbEta ce about sue oend"d axte be'11nc �>.e vate

bee cooy (9) are the c a �e £1ze but J! o�ooE lte t�ou�ht EJ w e wtll not 'lla�e use of

z Fo r 4:l, = O;v c v 4 from eount ton 9 in e�uat ton 9. them. In orof\ls lI ts BlRO alway s y 2 = 1.So ! 3 Sae co oy Pa.,.e 19 The derived ecc1ation 9 holde even fo r computat i:>nf of heiFht W e obt 11tn '.'ro-n hRr:r,'Jn1os R.. - - R,. r , . the touan 1t. y . h ee a 1 'I! d of 109 olane above the bot to'TI in which even furt'1er oro fll e, I' ' , I ' ' ' , l 3

n rr:iot of '1•Jsdr'!lt1c er.,at .\on I' ' '' even in every ot>ier oro file fr••ely laid do"· between orof1le I' h = See cooy Palle ?'.) a�d II,1f we chanpe the mar� as tndica ted tn FiF. 2 . 3 ( �)

D ie�cvert es of numertcal comoutationE are shown tn Table 2, In T�hle l,C ,1·1"\n 6 .ire 'lleaeures V'll•1<>s h 3 _1n Colu,n '"' are 1 t Value£ h Co'!loutt>d by e-uat ion A, and th\e for Rll va1•1si; 0� end __ wh�re te ,.nd icated the value co'!lou ed fro-n h4 ' and actually i:eaeured h4 • 3 Mi n '" h e t o 7 From the tablee we see t. at both na'!led v11l •1ea do not differ.Where valuee Apree-n 'TI"'leured snrl ro'llO'Jt"� ·:alue� o f h 1,; ·;e ry ,·> o

n differ it 1e rathe r· becaus e of the uncoT,oleted re so1u• ton of e oe c1 ftc ,neeeured R re 11en.,r'l.l l y n,_.1 1pably 11reater. T�e roaeo ! e t ".at we -neasure

11 nd z n h lnd th" vate , not d!rectly ln orof\le I,w>iere h we1Fht an

I t =O , ,� = l ,eauRtlon � 1 1 1vee very RCC­ cally Freatly tnterest inr . ore eente known values of 4 1. , v Then for lnstancee z = 0 ,1 1 , t ,v3 , 4 0 for urat e values . va 1oue r 1.!1 and p.The refore in Cha ot e.r D,I p:1ve an al to11ether new e,no1r- 4 1 .�cr�9:na:n1:..<:_�'-uat !·Jn ::," •h.-, cYater Body Between 1cal formula ,that 1B a formula of actual measu�d •,e 1·�ee .In t '11s I do rr :if�':_ I�i::_

The l e n,,.th of swollen hydraul ic ju'TIO ehould be c1ne idered a C omputat ion o! y4 whlch wse ptven ln P� ravra oh 10 •n Cha nt er B, ,,.ete, carefully taken ,ae the dist ance of profile I and II,beceuee only and values w'11c'1 are tn ·r i:..-t le 2 . We e t at.o a = 1. from profile I occurs the croeeinF of the torrent ial etrea'.ll tn rtve r For orofll e I ' we ta�e then stream,so against lenl"th 1 P as is ind1ce ted 1n F1F. 2 ,of dis tance ' T r :. See cooy Pape ?J shortened by e(Va1ue e 1 s p1ven tn eouation 6 and 6a ) To do eo howev er For oro file I I everythlnF le ae 1n Pa r1111reoh 13 ,Sta tement

-- ·- •.. the reeulte 1n the brac�ete 1n eouat\one 16 an 16a are plaln r1,.u re1 would not be pract1cal•• We br1ng up therefore F1t1,.ll, Ju1t as we d1d for Pl at� l".ydraul tc w"tch g1ve a whole group or (cate@ory ) u �1feata�fone ,dtfr�r1ng oniy 1n Jump,:>n a horizontal axle measured lrngths 1 P 0 (dtetance of or:, r 11e I I the measure of the ay!lbot ) • The measured. quan1ty 11 correctly tn d.tcatee one instance • of a whole catego�y.Compar1ttvely we arranie even a from the irate)and. on the ax te the suspended heupht of swollen hyd raul�c further formula from Pl atn f1irure and one n.amed quant tty. Jumo. 0 Table J See COP)' S = Y2P _ y1 (10) 16.Slo!)e or Too or Swollen Jumo. In F1F.ll we obtatn tnrornat to n o f great 1moortance toward a new ° We f1x th1a as tn(F1g.2) tdea ,•hAt lenirth 1 of swollen hydraultc ,1umo ts ltneerly measured by T See copy Pap;e 23 (17) the he\Fht of the swollen hydraul tc jumo. he atm of dtrectly p1ven d1m­ We br1np: uo the analopy 1n rectanpular Ax'e,absctseae 1 ° and tn1shed relation ta tg a 0 See co-:,y Pnge 22 (11 ) ordinate y2 9 -h) (Ftg.12).If we ae;,arate the ootnts accordtnp to o,we 0 ° e, obtain a fan of rays •hose evolved. d\recttons tg • are tn Table 3,Column If we had carr1ed tnetead or 1 into Ftp.ll ,the length 1 - .._,,; I _- ...!,.. I tv1�U11 ·�tues are 1n Table l,Colu:nn 12. we qd \ 12 and would have obtained the value ,Aleo even for pl atn hy - 2.,{ f we br nF up the values tg� a� quant1ttes to a sctasae o(F1g. draul t� jumo we - discovered 1n Study A, that tp: a � . Ther�_ occurs then lJ)we obta1n a hyoerbol1c curve ,whose one astntot ts �e axts or ab­ { the whole paeenge accol!! oanytnp: -,1atn.t- hydraul tc .Jum:> and swollen hyd raul1c ectssae p Jumo on the leneth or l!!easured he1ght or the lumo(Ft�.8) For p ,. 1 1a tg :: tp a (17a ) Pap:e ..,? " p = -.a ta tp: = 0 (Fb) See co PY (12) 17.Emoirlcaf -Formula for C:>mO•J!at ton or the (12a) II (12b) _Eepth of_Water_r3... Behtnd_ 'i_Gat ... Thie ·�nowledp:e Fives a p-reatly interest tnp tns 1Fht tnto rr we •a1{e,<. (Ftir.2) hen 'ro� eouat ton 1 7 enerFet tc balanc" o f' the whole man1 festatton as we 71111 show tater. Se,. copy ") Let us ooy rrom Study A,er.uat1ons �� and 34 ror y and s and Whe re °"3 = cotg a tF • 2 Values D3 0 are tn Table �,Column 9.n� \n Ftp-.1 .... we lay down See cooy Page 22 (13) For See co:>y Pa pe 24 ( 18a) 4 For ° (19 ) (t ) " " (10) (15) ., (Pa) ( 16) � • II.. .. b) (l (16a) .. t� ve The result of equat ion 13 ts a ola1n unair.ed f111u'Nc'. Then even e find a.lea from eouat 1-Jn d� anc! usn use enu9,t t0n .. 16, ma x1rnu,i; 5'3� cooy ( 20 ) p Pap:e ;? '":, (21 ) " (?7) 8 l�.Eoclrtcal Fo r:nula for Dtset �ncea 1 fro:n the O t�e?'l"18A tt t� a;nln oo�s tblo •o wr! t e G�.!.2_to •he_ Le,iet De ot h h 9-= See cooy If Ne :na�e trr w = (2-:>)

and carry out ln Ft,. l -.; to abscH�ae p :ird'n!lte ti'v, fro:n '!'able �

Col•J.,n 4 u�ti'IOLLE:�I HYD!{.l.'}T r: JU�• P . Se,, co oy ( ?'3 ) �. Decre11r� of ..'.echan1cal E:n-a!",.l_ Re fclvr·.:'.__ 'o!" The oroducts of cot p a t11w are t,luPtl""�ed 1n Ftp.l � b:; 11 c·1rve �onelastlc Katter. ------ana by ft17uroe whtch are ,tven tn Table '3,�olu:nn 7 I f t'ie ordtnate lines of ene r11y tn oroftle I H 1 ,., (F1 t . ? l For See c::--:;y (?'3a ) and 1n ;:>ro ftle II H P 1 0 ,i 1ecr.,as e of • '10 :nechanlc'll "'"·r rry obt !llned I I ( .,"" ) b�t'Reen 'both ?roftle0 . O therw1Se froi;: eauat ton l"• .:>ee copy ( �'.)) Sec co:iy (�4)

1 q . E:-nolr1c"-l For-nula !'or Co1n·.1t · nP' • 'l e Le'IFt Deot� ------______!14 If we lay down /F l11.2) the voloclty v ln oruflle 1 ,Nlth whl ch ls :noved A wqter sube t qnce See copy ( ?':J) I f.,llowe orc;:oree s�vely to lee ner veloctty v , which -::o •t ,en oresents 'I re"ct lo!l of a " fan of raye ,d1"fe r-'.,.. by n. ,n . s� tn Ft rr.1 ";, If ,;e carry out tn F111 . 1 '3 nonel!I.B t1c subst!lnce :no vt n11 ln th·,• <:!..i::-'!t1oo of the !'�act ton result as a Jertv1t've f unctt-:>n 8:¥ •· . 11 ylelds Carnot.' .. statement : "Loot Nor� ctren,th -.,131,:rht le <>'l'..llll t-:> mov• n See copy Pa p:e· '."5 < ?o) enc r17y co,noarlttve t.'.l :!.est velocl ty" .Thla statement wae used by 3ord for Where .. '" / me'lau rlne- 1-:, ss of :ne chanlcal enet'Fy by hta views on MBolvlnl" o water 'lttlues iJ. rare F,1ven 1n Table ,,�olumn 6,and tn Ftp.1'3. streams • . ·--- i.:x ;,n:,·.,tng Carnot 's laws !or I , , .i so See copy Ptl/l'e 28 ( '3 1 ) See cooy ( 26a ) ,, " ('32)

-- .- ,·· -..,,.,· ,.. .,,

1' _../-

21 .Decreas � o!':techan 1ca1 ::;;nerp;y of 1'"!. ain See copy _ Hyd ra�U£2.� and eo after lnetallment Accompanying ola1n hydraulic jurno,the decrease of :noc�antcal See cop�• ?ap;e 30 {'14) energy doae nc,t cove r t 1-ie val uefl!3 tn oquat ton 3?.Of th 1o ve :n'

to Safrane z for the fl ·et t1�� ,hy Stevena tn the year 1Q?4 tn The com::;c�H tvo '1Uar.t 1t tes fo r olu tn hyd rau lic ,lu!'lo, Seo copy Eng1 nee r1n� ��� Re�ord. If we use the eouat ton of cont tnutty 2-:>.The Decrease of Mechantcal Energy of . Plat:1 $en cooy Hy�aul le J•�m ::i i.:x orP.es e�_1.!.:_._ _" ?..!.. _!._e_ch�n 1 c!_l_ !'.:n&fL{ an r H in oroftle I. d equat lono of LJ iraultc react.tons fo r pr, tl&� I <.ind Tl �ttend lnR 1 \Ve determ 1.�e the � of clecreaee thus : ::>lain hycl.raul le ju-np {Study A) :;ee copy See copy Page 30 (36) 'fie obt •. l:1 tl-ie f:ir:n...- The f?r-nu la 36 we obta\ned ftrst 1:1 thP wnrk of Sea•ranez, I

have F

23. Decrease of hlechan1cal Enc r!lY of Swollen H,vdraultc "1p-ure 1- �

Jump. crenen and thP lint e of the decrease a . ,,. If ·ne lead for the sy-nb-:>l of vel oc tttes he tpht In Ftv ,14 s carefu lly c'.rawn a l tne ·,s'1oce .) l"C tnate

See cooy qc-corc t·w ·o e,,uat ton 32 an ' 'he l�ne

and ex,,reee or?:>t> Vie c )mb tne : r techn t'.:l"l hydraul tc or�ct.1cc .Ie 1'. oo :o:.J!c-:'.e ''n0w \.-,17ly •-, ,: ' .-,o rtcn

::;ee cooy ?a ge 11 {37) 'he l•npt h c! •>-,e '1yc'.r�ultc .u�o l,e. the lenath ,f cefor'!latlon? O;

I 1 �-:: 1,!.,� "ould 1-ie re be obtalne1 a �re•� ·r decrease _ - ? �hcee cue� �lons For li:nl..t 0 1,1.e.for ol at:1 hyd ra'.ll c umn ">y eouat !on 19a

(Y'a) I Wlll L�swer later. See cooy ?ave 31 Equat ions 37a, 35,34 , and 33 are tn effec .. are ln Ftp.14 arrani>ed to 'lbf c\Ecae _ 1 1.". T"lo orG1:1a:eu· O;s o For 11m1t p-,. nnd by eouqtton l� , d , �

See copy ?age ..,1 ("'7b ) of cont lnutty we o't:tatn \ -' __ .., /, - ,._ ,and 1.nC!er:. '1011 t, e'1 lit 1:>n "' -.:

For o "'-""1nd tcates t.'1e dPcreae"' �� '!lechan1cal ene ray .,,., who\.e See c:i oy ?ape ..,�

Lo t us JE e ��uat!ons 1� and 14 veloctty hei!lht tn or:i!'lle T ,and e'1ows v 2 -_ 0 ,i nd •>-,� 1'JB vclocl y .·,

" - Inse r• from e"'-.lat 1-:> n' 37 into eouatlon 'lq .,.

See copy l '• )) ,are traced ln F1P-.l4.T '1e r<" 1 E Insert fro n eo Jat 1 on 38 \nto e�ua" l::in �,

�ee cooy ( !, l ) 1� th� curve Fo r the 11:nHc , ThP ClJrve tn eauat 1on :55.For the l\:n1t ( .,,.(.,.. • :

See copy (4?) flllls betweon curvee for p which formul a we can also eas 11 y uee 1n the oc,,-.tt. ::in '1 7 h. e a8 'lCCO'llon:,tes e1,r.ll'!.r nonelaf'tle Analyt1c1tlly p-reatly lntere�tlr.p-ly we cou,c ev,::,lve th

for:nul a fo r . emu for Bl BO t_ hus: 'I? t e Se9 copy Prt P'e o "he -iue Et lon which ! h� d ,non•.t,::,n,,d tn ?B ?"!lP're. --,:, ?l .T'i!s nu btlon

Subtrac ttng we obtain, 1 4 See C'>DY i'9./le 3? (4:5) Al l cur•, .. � ln FlF. 1 :nust orlF1nate from th� u,��� w'1ose qh · .,.- !'e·rn e The r1ght e 1de of eauat1on 43 e'ic)we ho w .nuc'1 t -, ce� e of scl s ae 1E •\ =- 1 . T'ie mot. tve wqr e xol!ilnN tn S•udy A. "'or at-Pc ts�"'e 1111 l.s i=-r-,at e l' :han t he 1. 4 I Ehow curves ·.� h tcr. ,2 l--!o'.li f',(! ch&!1ue in the cr-_: :�,:e��-�!:::.T'lic · VRlu0 mechanical energy of a swc::.len hyd raulle �u,n o = len r,JJ raul le J·.1:no, �ec -i uc .. decrea6 s of th e mechanical energy of an uno,w,o1 . .b!l , a waye V'llues that ,ire t. '1.e r1ght e1de of "aatton 43 ptvee ,as t s evtdent l Fro11 fo ri:ul ri �� ,· u·Jpos ttlon� w� tch are .avlde'1t "r:,,: equat tonF 7 ..J 7t,13, '> nd ::>') we can c�1.r,Fe ::ivc-r eae tly t .:i for-null! �.,

The com:non ord1nate H? 'E �tven tn the ecuat1on 4. 5ee co oy

New formulae which were '1e !"e used fo r the ftrEt t 1:ne for �h1ch t� !1xc� wtth one clatn f 1 ��re (\n ''1e larp-n 'or11u1a)�f ·'1e w�o· e

swollen hydraul 1c jump show ol atnly the anl'llyt 1cqlly s1ngular1ty of both catei,01ry of the '119.nlfeettons d�ffer tn;, cnly ,n 'he 'lleas u�e of •he

man 11'eastat1ons ,1.e.hydrau1 1c jU!DO owollen 11nd 01 a1n.The olalr '1.yd raul tc .A �tx�-d 1net�nce from th!i cate��ry ts g1v�� � vslua �f a

etrwl e :-.ieas�.red c•.1P.r,tt•.y ·h1::h ,t �.7hf _be eas 1ly jump forms only the lower uncroesabl e 11ll1t of t'1e swollen hydreul\c jumo. fe r � ns tance :; 1 ., ·,

F. 5Ui>WARY. OF Il'NEST IGATI�NS chan�ac :or !inat her,� n a combln&J eauat ton.

tncre11ee tn he1Fh' �r at :::>4 . The 1.swollen hydrl'lul1c jump occurs at an ----Le--::r---eaJe cJf-- ;,,.e-·cha--nlcB--l- --Ene----r!"y-- .Jf-- !:;w---ol -le--n - he1ght of pl a1n hydr,,.u1 1.c jump. ·�yd ra ul 1c J·.1,�o Re eol ved tri � :, f !,'. e chAn1cal an enclosed ______:!:l'J•?f__!'V .. 2.Teete conducted 1n the ye�r� 19�� snd 1934 were s eoarsted by H \n oruf1le ! of Pl atn I ------lly----d !"'ul--1c-- J-u-mo.- the e 1gn of torrentness ,and by measure of swollen P. In th1s study Hi Seo cooy ( 3 => ) 1 B related the resul t of 56 tes ts 1n wh1ch w1 was 1.6 to 19.9 and P was 'c ,. -- -- �-. '. "' . • :,.7 -· water wb1rl. and de rtved fl'om direct measure o'f emi,1r1oat-· for�a l T to l;;l to t. 5. Value of 11 = 1.9 acts as tbe dtvlston wb1cb 1s manifested 1n 1 29. eauat ton �. 11.Tbe decreas e of me�bantcal energy for ola1n hyd raul ic jump ,.ay accomplfilhing the measurment of swollen pit was possible ls glven 1n formulas 33 to 35 1n i formUl as 36, fo r swollen jump, fOl'IDUlae ., to present a new formul a for hydraul ic Jump,swollen and Pldn,and sbow 37 and 3B 1n % formul a 39 to 43.Dlagrams 1n Flg.14 'lnd 15 �1ve a complete the similarity of both man1feetat1one . Hydraulic lump,unewollen o� ol a1n Picture of ene rgetic balance of plain and swol le� hydraul ic jumps. dan I ts only a real ins tance of th. e lower. 111111 t of measure �f.P.:,__; • The upper their 1nterestin@ relation. limit /;-=-oO gives an 1ntereat1ng theoretical discovery 111nd enlightens

12.For swollen p 1 . 25 covers th e decrease 1n mechanical energy clearly the energetical · balance of the whole manifestation. brought about by the swollen hydraul ic Jump s1ze"Bord 's loss" whtch ts 4.later whirl about hori�ontal axle above the maln stream has a s olved by equation 32.In 9quat 1on 32,v v 1nd 1cate veloc1t1es of water 1 2 throu,:rh now 1 � which chanires from oroftle to 1rof1le,increaeee with the Which aro co parabl� to vel ,cities for ol aln �ydraul1c Jump�Bord 's loss" m measure of swoll en � 4nd wtth symbol Y1 • 1nd1cates also •he decrease of mechanical ene riry which occurs �t : =s 5.The top of thte waterwh1rl ,espec1ally at greater P �a concave of :ionducted nonel astic bod1es ,·o.f_=r r11Bnt llhieh,-it1- foUow-e4-:'by- ��h� a� tt must conform to acttone of level olanee of water turninir about v1 and v , horizontal axis . ;:,

13.All for�ulae were der1vllld eo,that they are ;lq ld down w1th 6,P1ezometer meaeurments made 1t oos eibl e to co�oute the de­ two v alues :unmeasured ontn numbera.., wh1c.ti charncter1ze the whole cateF.ory centerinF pressure on �he bottou and the epectf1c welirht at l eas t of the man1festation d1ffer1ng from each o�her only in •he 11easure of closely from equatton 3.The spec tf1c we1Fht of water of dlm1n 1 ehed water J !he 14--,..J>.+[ � and o:1ly a c1np-l e meacure t�'l� ·1s a na11'1Cl cu,mt tty whose whtrl fans dP.ctstvely below )-1.t le smaller as o 1e lees ,larper as � , :J.. • ,,,,. 1 own v alue !a suff\cier.t to t'f'ft

8., 14. All formulas for e·.der � to 15.F::ir,1 eo•h of sttl­ ci.The le pth of h:1 draul tc ., um') tr f!iven P. B 6 ttmee the pro­ t'.lrrentnese i.11 n.n n n

! np oool I lay donn for suitable overtJ O'J1nf! p _ 1.2 t) 1 . 4 for noet ti�ct of he lpht of hydraultc •u:11p; fr::,m it was derived eauattone 11 to l61t. danperoue hydr�u1 tc cutetence. lJ,For comoutattons of helFht o f water h� behlnd 'he pate, thn leact deoth h4 ,ltc '.!tetanc,, l � fro:n •ho p-ote and for slopes ot' toe,.- :).f 'l------· . . I

@) I I CD ® I

'}-4 • 11', - -TZ4 -0:4 g 14V4

w..?1.!!'__ I M, =6.79 , q=0.0 866 m3/s 1:9�2 ___ ! J'.\9!L - : 9-Jl §:i__ _ I' �§} __ _ : _ . 9-_!l§ !_ _ lh. P• 2S (f , ,· ----- 0.535m f I I! : : t,.. ,------� ------2D 0.405 NI � : I -=-=, �-"--,------t��:::-.-_::::::-_r-.:-:-:.-=- 1·6 !1 .. �-"";;::: L: ____ ------,- - - --� -- Q2 l � 83 .., �h3 : >,.' � : � • � .,:_ - -- . ! � i � � � g 1·4 Q226 in I • 1 I 1 1 0 IN,.._;;,-�-.:.-.:: :.:.-->-,-�::.:::�------, I : I I a 0 I - ---- t,.. ____�� ,-..:-:: : ,::..J<:::--·-�� 0.146§ , -- .... _ ,.._, __ .,. �I.Q i i a "' ;} d I -r----�--=---..L.: a::� .=-rn�o------.::-::-� ,.r_,,_,,:.-A--! J gt i I l ,i : l 1 1 + ' � * I' i 0 :-3'-.-,,;,i,-;---r"-f : , 19 ,a. 11 i.,. •• ------usm - - -- j i'n f ! - 1 ?-, • Pi e zo eters I to 19 i p 1� \ :., ______1.4�m ____ ('?�-"'-�- - -� scm I l ! i "lt___ : ____�_-:: -;;;;,;�=='.·�'.�_:======�=��---_-_-_======:�=�===:i L ______l------��:-_-:::-=��:_--����------��--��--��-:_·_-_-_-:_-_-:_-_-:_--��------=:i FIGURE 8

HYO- IOC6 l 3o

. _, ' ,_ � :·-: 1:•;·, f-- •• '_·:.J;�. �- •. • r\ · .. -� -- .. T . .._. ,. . . ':':� "·.,.. .:-

M,• 6. 79 ,. p • 1.2 , q •0. �866 ml s II 11111 I I \._.• (� ...... , ...------

'.

;� ------·-----L .,.. ... -�:: :::::::-::.-::.::::,- m ------,------·· l •1.4 5m ··--

1.0 2.JJ 3,0 4.0 'mts .. VELOCITY SCALE • FIGURE 9 p• 1.2 , q •0.0866 m'1s

.. I ' I-�

2.0 3.0 VELOCI TY SCALE FIGURE 10

t

FIGURE II

0.20

I.I

FIGURE .,.'...\ ·JI

0.4 0, 10 2.0 10.201 lO

1.5 j0.1 5j I"\-\ 0.3

0.06 I •

1.0 J0.10 02 0.05

b C: _g l= C: "'C: C: _g _g _g 0.1 1:1 1:1 �o �pc 3 1:1 C: ot a: tan a tan 0 0 D, , w 0 0 <.> <.> cot a fan n - A oj t t I.I l2 1,3 1.4 LS 1.6 2J) 2�J �> p FIGURE 13

1.2 ,------�--�--�-- = k1· (k 2+ s)

I.I cl .,, - i:!J..=...vzl'. c.HP"I{ =�-�2 g = b. B A Hm B · V1 +V2 - 2 g w = :!'.!_- �)3 C 16 A-1- = Yt A Ts • � 1.0 _Jlj__ M1= Vgy, = k,-(� + d3) Q9 H" [ • l 2 4 I p P = y M, [1 -p2A_ -I)' " 0 (A -1)- 1]} 1 fr ( 3 2 0.8 = k1 { 0.1 r•H�= •f M� Q6

05

7� .��-"" • Hp %� I: -.4' I Y 'J I I I 0.4

0.3 1---'--+--+--+---!A-- c.H'P= I t A�P

0.2I----+--� . )f ArP-/-?"F---+--+--,....-+-.....---1--..;.._+------i :x: ., I · .M I 0.1 I ��:,c-·/r/tl _:· •:._+--+--+--+--l---+-l-�-1.._j__ r, .---.----,,-;�"1./ , I I I : I , I 0.0 g�..,-'::f::tt'3 ,�. --'----.L..--'---'----'---'--.L.....,__._.L..._,.__.'--' 6 10 _· FIGURE 14 _,._ M , 100% � I I i � 90

2, 80

70 .. I 60 \, • 50

40

30

20

10

I½ 0 • 0 3 4 ,7 10 II 12 13 14 15 16 17 1 8 19 20 __,.. M 1 'FIGURE 15 HY0--106 '' 0 . - r I '

Statni ustavy hyclrologicki· a hydrotcchnicky T. C. Masaryka V Prazc-Podbabc. lnstituts hydroloµiquc ct hydrotcchniquc T. G . .\l asaryk de la Hepuhliquc Tchccoslovequc a Preha-Podbabe.

Pfcdnoste - Dircctcur: Doc. Inµ. Dr. JA;\; S.\1ETA NA. P R · A C E A S ·1 · l. ' D I E . Cislo - '\o. ., . r a Vall:\ CI I ll cl t' s. 13.

(·

-Doc. Ing. Dr. J \N S�ILTA�A: EXPERIMENTALNi STUDIE VODNIHO SKOKU VZDUTEHO.

Ltucle expfrimentale du ressaut noyc. rcsum(- en ( \ \'CC un fnm�·ais.)

. n z,Jitstni otisk z casopisu · .Zl'H \ Hi{EJ:'\E. SLLLBY TECJ -1:'\ICKC", (roe. 193-t).

S 16 obr. v lex/11. Awe 16 fig. eu lexte.

'\ \Ki..\ lJl..\t \ l. \ST,i\t. - T!S!,.01 Iha t:IJ. CHI.GR \ AS) :,;A \ PRAZE.. t93-t- . 'l

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t ·r.. f/ 1.Ht&6fo 111' , . Ohr. 7 . .l/, r, ,!I. ,, l',111k;i1.i jt·=.tt· na j,·d1111 ,, k o In,,:--t d 11 1 t· -i. it n 11 .--:---- pro 1 rid i: n i p ,, k II I'- 11 11 ,·,Hlnfm -.k,,k11. ' K1H·fiei1·nt ,·.\· t,,k11 J >t,d --1axidh·rn l' j•· :--, ,11i·i11 .., k1 11·­ fic·it·t1t II r.n·hlo.. tniho .: (zt n'1toH'· lan) a k, wfit·i,·nt 11 k1111 · t r.,k,·e 1 . Ztnl111v_\ k;K·firit·nt (· ini pod l1· I A·--hro:--t· 1 1r1 1 mat,·, aZ 1.m1(·nl· , \·�k,· tlnt·nl· O !f!• aZ o-!17. · · K,"·fit·i1·11I ,1 pro ,:_\· 1,,k pod o::t ron hra111111 a jinah :- j1·dno... 1ra ru1

1 · Z11a111t·11a lt·d \ h,,,., dm1!,1 " ' 111,-, ,id nii. 1u 11\if, --! MIil_\ I/ , ....tt·. , j,· L11d1df11,;, l· i--1,, K, -"·(i1·1,·11t knnt r.tk<·•· pr-1 1 hy-tn11n_, l "'h., 1, 1..1 -ta·

, 1dl1·m , 11;1-..i·111 prip.,d,· J•· , ,,, . I, , 1 /, �· , ' --.-- �:. ... •

ti) Pit o I o v o II trII I, k u II j,1111· 111Hili r.vcltlust i 1T vncly V pct i prlc 11ych prufil,·di L', I". I'", l"" U. H mcz h I,,: 1·11 mi.,t c111 ,wjniHHho pov1·ch11, VypoHi'me 1ll1 pro 1 = 2 (ohr. �). l'rofil l' Ii.vi polo1. tudy vc vzd,ilcnoM�i t• od st11vidl11. Ost11t11i byly rovno­ 1T mcrno r()zrlcl<'ll\'. V k111.dc111 profilu hylo mcfouo V peLi ., -h.- 1 ) . . ( :! • .11 svi•liclch, , kn;,rl,- svislici v jcdnnt liv.�·t·h bodcoh vc r, t - (} vzcl,ilcnohlL"ch po :! c111. Toto podrobnc lmdovc mcrcni ftJI = . = (]Y1 \ gy1 h�·ln vykurni110 j1•11 pro rndu VJ I. a lo pro p = I·�. I ·-1, V� fikoku prosti·m li_,·lo 1110:i.110'm(·ri ti tolilrn vc dvou 1 ·•l. l'ri ) = , ...v-, :;r; -2...:...l· !l. (:!. (Jrofil,·ch vzd,il,·111:jsich od ,tuvirlla. Blizt· sta,·idla velika

j I o r g n n o k y II s o n s t II I i. i r II X e Ill i1 1. (' V �' l 11 d O \' vetsi I" 0 7. S 8 h n C Z p ,c

h, .;koku. B. Hrzi'm ,·odnihu g . . , . .\[ ii r C n l' h O d ll O I �- . 111·et'll cl , t' m fl z v otli,·)• pokns hyl i1 plne wm Jedn mrh-nym nt1 Th -nom d 11 111 i: prutokcm q �-� n :;· m i h o n t I. slou Obr. 8. otcvrenim h, stn vidln (l>1 h. sonovc prcpndno a 111(·­ . C' Iic i 11 �- hyl�· p iwnt' 16. 4). \"secky o d vis I e , 1. ,wndnty. l. j. pro J' = 01,r. " pn·,1,t,l\'IJjt· p1•li·l11.,· h·z pfl·su(· podlt· 1111·rl•11i jcjich hod.not�· pro skok 6 i-eny ; jsm,· ): ' 1 .nt�· z1.· stncli<' A . .\IN-iii JH•kueu z rady \ II. . 11 = fl·7!1 a /' � I·�; v 11!':m jsou byly ,·etsinou prc\'7 ·cl ,. i· it k 1.· m ,·)·i-knhlud in�· p ri i ohrnz.v roi'.dl·lt·ni ryehlost i. :tit· jt·n \"l' R-Vi:-.lit·ich un1i:-:tl·- n) Spi {· k o v y m m h,. · .. . ,·�·skn hl11tli11�· w a111,·idk·m 11_,,·h , ,.,, zl11h11. (Jl,r. Ill prl"rl,tavuj<- :; r_,·chlost11ic:h stnvidlC'fn h.,! (obr. :!). "• ,·:i·�kn hl11di11y w vudnim ,, i,lic pi'i,·ndiu pn,filu I' 1. tt·ho?. p"km-11. ncjnizsl poradnici povrchn · · ll. ll.. -. ). l'ro rady , 11 js1111.· kokem y," (tuh . I. sl. :1. d1. . ohne 1.nmHili eel)°· pon H. \' ." i.· i :-- I , n i p r II t o k u i • i \' (Jd rl i Ji II podr d�lkn ,·nd­ 3 1 111 m(• ri t kt' Ill : cclkoYO\l . b) De I k o ,· )' 11L-nost prn· , i r u. dutcho./•,t. j. ,·o

:1· •' '' < ,. �- " --- 2 T h T ro T·•h11lk11 ·>•• ,+ ;,. i, avi�lio,p ­ ....� -li kin dnc r: i�t i ryohlostnich . Hl- 0· 17.)0 1t·21,i0 tnk� T, . ' . ' •• ..HI .. J 11-,jf JHI> ll·H.j.)O fHi:Wo 11.:14 10 ) 1 1·a ) 1 4 1· 1. ;p, I I:? 1 (HliO II , 1 ·0.jlJli ll1- 11:!1';'0(1:_t! I ·03flfl t ·04 St i.L·llll' u1.a vi·iti: I kL! dlll 11·'"',0II (1-!)flfl I ·001) prut,,=ku i 111\r .I • O :!fi lll Z ,·ykonan�'ch mC'h·ni rom I , Ji, Ill II J li:?I) 11·:!lfill · i. II J:JIJO fl 170tJ 1 2:?110 1) :!-1,jll ost i j,, i3 i, " · ,, ,, ,1J11 · 1· · a) S vc•lkou pi-iblii.n i· 11 n ;, . t\-j\l 1 otl profilu k prnfilu p h) i je velici1111 J/ : 'I 1 IBJ n n-1-::! 11-tnH i IHJ(jJ I O·it2H8 ..\utipa :-te 1.nakl�111 , 1 e) r n st c :t ntirou ,·1.c - . 1 II nH1ij 11-tt,7:! 0-111'>!-tt, O·O�(jfi · skoku j,· 11 vst n t i o q II Ui-,1\U � i I cl) poh�·hov�· rdim , odniho 1' 111 .. II 1\:{t)II 1-1,1):Jfl 0·7H00 11-:r:10 ,, ., ti .ill ,·1-f\:!:!tJ I} .·, j ,j tJ O :!fiUO 1\ l' I' I\ i. I I 1·, 111 -. 1:1 · · 1 , l ·IIUlti I HIU7 l·0:14!) I ·l1.1:; im :111 O 11:!i IHIJ'"', O·Olt1 IHJO ( ,· iru n�d ,· last n 7. Re1. im vod 1iho J.''•, '"Ill ll·:!:!!fll 0 :!l:\11 11-:l';jlt o.:w.10 ti t' m. o 111.=-,o 11 :! 1.·,1 1 f1 21il11 1 IJ :JflUll prou 1 1 · · · 1\ 1 hlan1im .. · predstat ,· it i n,d11i dr 1nJ ,, 111' ... II 111}; 11 O•lli:J:! ll·OH.i i fHIJUH - [w.c•1lll' si tcd� o. kt,•r,· 1) 11,; 1 lHi... 1.)7 :t i I i: I e" .. "1 "o,n:! ,, 11,un - o l ti i· ,. j i · i s ,. , 1 ti n proudcm ja ko uknzujl' nttzornt'· ,·, ,11 .. I 111-;11 11.,:, 10 11·0">20 11--1:_tJ• , 1 vicC" �cn1Yi l�·t·h pti:tu. jak I ti 1·, 11, II l�;,11 It· -, I ';11 0·,1 7:jll 1J-:Jo.-,:J jc g\o-i.l'nO 1. 'rut11C'rnc· , ic,· 1 . 1i1 · mi i-e,.y uprosth'd 1,·\csa l ,.,,., ,11111 II �,Hq II :J11,0 f O<\:?!fil f)-;J:;:30 obr. :1. Pi·ic· 1 i,1 i '"' rc·hu / !/ j 11111·11,\ kfno-.1 1 d1.1h., , o1a1 1·ji.-i '" i·:i.-..tt·0k_,· 111 . :l\·;�n k sajic-im J>. Zej111,•m1 I 1 vi1.li·ji 1 1 ivaji hladi1111. l'i·i 1.u,t.1L1 \ i.d_, 11,111 JKI\ r. .Jw111 hL1di11_,· . ,J :--1,u t t·dy knrn 11t,· . kll'n·· prnt rlu =- . h\11b( lke . t t I, f taken, l11ji n>1\11i11111 ti·lt·- 1 / !/ j ,· ..11 ·1.. _, r11, !111, i'· j1 l1ot·h., ) ' lo,·h..-1111 i kon- c\oniit i· v1.d 1L·h a 1dc- dl• ,,:-�· - -lnl· nt.'t \· i kldl· ll\ :,,:,·i- l,; .1 , u i 1n i , , h I 4 ' d 4' m k I, n d 11 u'. in1pul:-:y. 1.e:-:t· pntvi l I: .., r"11n 1111 pl1 wh1111 j,· , ,th i pnn·c-110,·1·, hladina. kch· - v o tl II i h , , , i r \I ti.th 111,· n-,1� 111,·, 1 ,·11,111 1•1,·1,i1ni -tn m j,· 11. P1 1\T(."h( 1,·,i R u , . i, u v l· p l u e h � _ 1 · �- - • iru. hl.1d111.1 Ji· 11\ -..-111 ,.t,,d11, .1 l'l. .1·h.1 I"' , :dc to\ _\· m plo<:h:-i.n1. 1 , uly , t· , u1l11i11t , tt.·nrl't ick�· nu\l·t·ni , Hp--.111, 111 1 n1111,d1 1111... ,,1 1 1.1, 1d1·lrw ,1 kliclm'· t1t1it·,·11i f,;kdujnH· 111 l "'"'"i . 1 1 1 ·(·k11 111 (<>hr. -1 ). \a i k11i 11w hm1 111n11 c,i,1, i 1 . 11;1 ..t,1\ .1 1111 , y ...... j, Ii /' 'ro 1_, pnp.111_, \ ' ka111je (' ,. I_\· \'�·t · l 11 1 ·\d,·11i .,.!,th-di\, -ih . · r tii.<' !I a 11i111u IP 1 ii·ir_,, p 11 \ r 1· 1 , y .. I 11 \ , . 11 11 ti kn II k .i \ i t 11. T1 1 jt·!'t l 'rir.n·hlt- 1i • p 'ir� ,·\th·1 i tl.tjl · ld \': !'\ .-11\. ,,t t l\,i 13 1/. 1 / jl' ,,b,

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I' o r r . �lne t· :)' Z 8. V · o n O V y 7 , a j oi Ill 8 oV o u . 8, 7� = . 5, 6, 7 js povrohovych 011, v ob znaku v dnih sk ku stejneho fotogmfie vzduti p 1· 2, J·4, 1·6. .M, =6·79, ale ruzne9. T mir I yk d

o n o. o o a k y n a k o " ,,,...... ,., ..JL .. Ln t o tlaky 1111 dno: v dnim sk ku vzni aji tyt o Pri o y v dy, avn i m pr ud u narazeji Msteo oa) V h I mi oasteoky ryoW sti smeremo opr uduo pohybujioi se vetsio 0 i. tymz smerem amensi ryohlost a v dy, ktere se pohybo uji a ho uti tlak z k lm na pl ohu m·azo· Musi tedy vznikno sir! n filu. P nevndz tlak v kap line se sok v one pro strany, pr jo.dri se tento tlak zvysenim hladiny vseokyo o puk prlslusne vy y "' povrohu ; tluk na dno je roudu v lneho k o upeo v dy. h sl o f V v hluvnim p ' Budiz speoifio a vaha v dy l i•o '!'. d lejsi casti v{rove )'a• \' oi-ejsi ., speoi ioka vaha vodyo 4 o o + + na dn Pak se projevi hyclrostatioky tlak Msti )'•· o o piezk metru )'iY ys sY )'•Ll•Y· vysk u v dy v v; \ I �'t -" I I I -!- oi nnikaji

Pro1 v o d n i s k o k v z d u t y z ,. n d y VII, Je tedy celkova piezometricka vyska. sta.ticka P M = tl·7lJ, /J = I-� bylo vzato y, ::e I a pocftlino z z r. (obr. 3). )' Y :1c. Hodnoty z jsou v tabulce 3 zancseny pro profily P = 1 + yadaY + y,d,Y + yz : II, ( I) I' az l" ". Ubyva jcjich velikosti smcrem hlavniho Poradnice l\a,ry mechanicke energie je dana souctem promlu. Ped ri.me Rtcjne velikost i z i pro pffpad, kdy 0 vysky statickeH Pdynamicke p = 1·2; pak vypoctc-me z r. :la hodnoty \, 1 P-y -,z = + 2 (av! + a311s2 - a,1 /) (-1) • = y {ad3) Y .dy 4 a jsou hodnoty Coriolisova (,[sin, jejicihz Rk11tdin<'.• kterc jsou zancSC'ny tab.v 2. Nejmen/H = 0·80 kg/dm h0dnoty jsme pocltali pro hlavn[ proud pro profily l' pro profil I'. ' 11,z I" ". Jejich hodnoty jso11 v tab. 2. J�o11 v oelk11 0 Rpccifickc0 v,i.ze vody vc vodnfm vfru nepatrne a mozno klasti a==l. uzadnimc tcdv: a) je tfm lllf'ni.' l·tN·h ;pcciljc:�c ,·;ih_,. )'• • jso11 Rnnd ve sk1 tec·1 ost i pon,·kml po ,·r.dy jl'n 1,, ;,1 I. · Y fl rm.nc;3 jl' ,icsn,ulno vsak to ,jist iti. l'roto kln([nw v:l111l,• II (· II II ll O (' 11 l 1)1ch:n_frh , _,· s<·k 1«wrchu nad,· dn,·m . 1 k,i·ch , . d111'. !/1 • cili i(· rn·jnil.:::i l,ud hladi11y / j,· nade 1u·j11 ,-n�i !l­ v profilt'ch piezomctru :.I n;,, 1:1 (uhr. ") t_\'tu , l,.1: - ��:1 \"1.d:ll1·1\111 :--l l' rni11i11uil11i p1 1h1U11il·t• h. 11d :-:t;1,·idl j · 0,5:1 _ (Hi:l>i. 11-,111. 11,,.,�. 11-�ni+. 11- . 1 0-:11:l. tl·-1 1-1. 4 1 ,i.d_, 111al·11l· ,-t-1 :..j r1t i Ii yzd,i.l£·1u,:---1 11t-j11u·n::I 1u1htd- rn . · . t 11n l 11-s:iu. (H!�2. 1\ !1110. 3 1111·1· ,11 l11:--1 11iho pn,11d11. · . ( 1/ :t-\11•1. P ,· odni ,kok pro,1 .'' z i ad11_,-!mH.\' . · · 11 ". \/.,I.ii, Jf111!11,,1u , \"_\"JHW11·111t· taktu: 1', dui.ll1l' 1 l·r11l· k · = I) j,011 . huclnoty ;·,' ,. kj! dm run1i·i , 11-!1!111 ), ,wfh·i1·11111 k11n1rak1T no:--tech po 10 <:nl: ll·/"'1111"'1. U·�-l:�. n-,,i . 17

1G ,,

., = F 11 1 t· e .J!.!.. jinnk (ti) �1.n,ll·nw si (ol,r. :q ti·I,,,. , nd11tl·h11 w1d U <1 skok11 E "" 1/1 , .. o ro:1.dt·ll't111 v prufi l1•111 I , t· dvt· ·1&�1 i. Lc·\'011 (·ll,;t pft•d - n ,·nlOCitcjmc/1, =podle mcrc-nf,111. = ktcr,:\ jsme k tomu= ofli ,.;ta,·11u· �i

i' {:,!/ - ;(1 1 : I / 1!/I 1 ·.1 ,,,;·,,,,·a> Koeficient Yyt.oku pro YOdn{ 8kok pro�t _,, 11 ,·zdnt.<· I 1 ./ y�·chazi pmkticky -to111.t• hodnotou. Kocfici<'nt kon­ ''' ;· '1 ' • ''ai'ai'1 trakce jeodvisly od ponu"• ru t lncnl· \'ysky k ,._,, sC't' v�·t<,ko­ l 'J 1 u . '•·'' (!, Yeho otvoru. Tia en' vy.:\k_, zt st,irnj(· podk· pr<'dcho,.ilw K j,·dn,,t l \_,· 111 in1pul-.u111 1 1hp1-.111i ,,. ab_n ·l d ...,L tl It i'1 1/ ,. 1/ ,..:. pro skok pro.•ti· a z ncho orh-ozcn�· sknk ,·,.du t �- stt-jn�. :-.h1>tl11 pn ' ' J.tdr,·111I 't r ;·1 . e · Ztnitovy koeficicnt rychlost ni j1· nd,·isl_,. od tl>1t·11i· 1 ° ,·j•sk.Y. r sp. od kocficic11t11 kontn1kN·. Oht• 3 zu,-1,ini 11 11 111 1 ,. H , 11 i \ fi ll stcjne. Zmt'·n�· za s 11vicllcm pi-iru�t k,·111 lh 11 uhu11 III :t 1111 ., d rod \ 11 k at r1 .. It n11 , 111 ,i I 7.a ,l •1 1 ·1· pusobiti pouzc ncpatrnc t1'C'nin1 1111 plui

Vyfeime ir.e srovnalollti R1 = Rn velil'inu 1'a jako Odvozena r o v n i o e 9 ,,, a t I i p r o v y p o c c t kladny kofen quadraticke rovnice v y ii k y po v r chu n 11 de d n em v ktere m­ k o Iiv z dallilcll.pr o filul", l"',l""ivkai­ 1 (8) dem jinem profilu libovolne polotcnem mezi profily I' ks = y (/IY1) - ; q 1\ II, zm(mjmc-lioznal\ onl podlo obr. 2. v h; 8 Vysledky 61selnyoh vypoottl jsou uvedeny tab. 2, V tabulcc l v sloupci 6 jROu m6fone hodnoty ha, v sloupci 7 jsou hoclnoty1 h' kde je poznamcnana hodnota vypoc(tana jako a pooltane podle r. , a to hodnota skuwcn6 mi'lrcna h,. Z tabulky vidlme. 7,e pro vi\ecky hodnoty .M 11 p. hoda mMene 11 po­ (1:1 - ��) oMc jmenovane hod 11 o t y s e m n oho n e I i la I. llIt 11 n e hodnot y II, j e vcl m i do b r l\. Rod­ Pokud se liiH, jo to pf-il:lsti sphie nedokonulemu urfonl notyze m6fenejsou po vl'ltiiin6 n patme v6tiil. To je pro , � spoificke vahy y, a tlaku z, pro' jiehi vypooot mamc jen jsme mclili h, tt\sn6 za tavidlem ne presne= v prof1lu I, kde ha je jiz o neco malomenAI. jednu rovnici. Rovnicc ll. oro r(1zneV J/ a p. Proto ve stati D odvodim zooln no,. i: cm pi ricke v z or­ 14. Hydrodyn11miok{1 rov11ovtiha vo - _dnlho e c. t. j. vzorco podle , yMINlkt'.1 mcreni. nich nepouiiji t6lesa mezi profily I' 11 ll (obr. 3); vypocet hoft·ji

Uv_azujme pHpady z rady \'IL JI 1 = (l-79, p = 1 ·2. D. DHJm u sldon�· pon1·hu nduteho vodnihos skoku. l 4. l 6 (tnb. I a 2. obr. 5. 6. 7). - · · = Empirickt' norce pro hluuhku rnd� h zu stavidlem Proi profil I' j<' podlo statis B. 1 u pNI nejnw1L;i hlouhku "•· ]' = I; Y• = ]'• < I: i i, = i; z = O; =:,> 0. V:vi><>Cei- y,.·

1 = Jh,) (I !I · · J · = � q1· +_

21 ,,

,-,

(vzch\.lenost profil11 U otl stnvitlln ) 11 nu osu N,·i�lou · Tui;:;'lta S. vysku vodniho "koku n.duteho tgi,, ..,.. tg n - p Y!' -h1 I• D: 001 1,ln1go cotg ,: tg ,,, ---- I• II py, -y-, • = yl - Y1· IP cotgu: tg ,'l -i ,- (10) �·� 1: --i-. -- I - V obr. 11 dospivi�mc k velmi dulditcmu I tg ., novemu po­ lg 3.. �6 �-="° J/.J d znntku, zee u ti I k a /•a vodnihov "koku ,·zdu_tcho jc Ii­ n c 1i r n m Orn v i< c e vodniho skoku vzdute­ I IJ·fi(J,10 lg , .. ho. Sml\rnict• primk.,· 111hi�·11jici zrnincny vztah jc 0-(lljllt) I O-tJr.:111 O·R7ll O·tJfi:ltl2 IHl-'70 CJ· 1 720 5 fJ·flfl- lrifi 7 8 1 /_ ,· 4!l 1 1·5 0·0445 l,H1:J:iO I 0· 111:l I Y ( 11) 1 · 1520 0·100 tg a• = -�• , = co11�t = _:_7; · 1·1 0· 11()11 fl-21:l I• :100 tHO·o:?7ol!l65 I 0·07 10 0·2:?HO0·111100 0-11-1 11 0·4260 1 ·2 00·0840·02l fi IHllU·CJMllfl 10 0· 11411 11·1:?HH fl·OJ0·0"47H:i O·fiMO IHJHti� 1-:J 11 U·1)·:IJO1 4111) tH17SO I Kclybychom by H vynesli do obr. 11 misto I•, delku U·fJll li, iiI 11-:l!Jt)IJ I II 1·4 o-:IJ Rfl 1-0:120 I ;; 1 I • O·:W71, IJ·U411:1 - ti '\ ""'' k j f' ti \' ti [ /P - e, obdrfoli byohom hod11otu :iuo ' 1·6 o-o:1su IU. S k O 11 I' U \ Ch Z t.J C, 0-0:14:1h O S k Ok 11 .1 ·271!1) 2·0 11·2811' I l·ll8f�J pro skok pr ty v�··l't rili jsmc vo st11dii Atg11 = 11 - 2·6 0-01:10 Urfo1111· jl'j jako. (nhr. :l) , ... ,,.1:1 I 2·11!1/0 (Ii) D O j O S ' t l' d y C {' I s· p I' C C h O d p I' i S k ll k ''. p r o s t n1 i v z d u t f: m n a d C l cc ll m Cr n I· v �- 8- · \ )'lWSIDC Ohdolme do jll'II \'f)tlhl sc•ck_,. /P U jlO· f·ndn cc ! e' "" (ohr. 12 Hoz1H,li111t•-li hocly putllc p. o e v o d n I ho s k o k 11 (ohr. , ), Mi � l -�· ); ohcl,1.fmt· vc·Jtr papn-ku. i1d11. ,·yro,·1ian& ,m ··rnice lg;r ) (I:!) I• =. (µy, - y1 <·otg r, - n ,,, jsou , . 111l1t1I<·•· :1. sl. �- J1·d1101 li\'t' hurlnot ,· jso11 ,. tab. 11) 7l i'rO p = I "' 1; (y, - y.) = n � ( 12 I. sl. I�- \'y, ...s, ·111<·-li hnclnut.v tg jako poi·adnicc 00 / ';.,. 00 (1th) k (1sd·k, 111 " p = _ i .. 1> _ (uhr. I:!. 1:1). ohclr-i. inw kf-i,·kt1 hypcrbo­ lwckou. J<"Jl'l. Jt'd11011 a:..ympt,,1011 jc osa lt:-:t·C·ek JJ. Tent o po,.11 att' k cl 11. ,· ,. 1 mi 1. " j i ma ,. ,. p r u­ O?O h l C cl d O (' 11 C I' g C l i C k L' h i I a· II c C t· I' I i, h ti Z j l'· \' It, j ll k II k fl 'l. i p O 7. d l' j i. ]>i·cpi�111e zc �tudie A ro, ·nice :\:\ u :\ I pr1) !It a ·" a poloimc ors A \ t - :; JI,' (1:1} ( 14) ?I B = ·�,' (A -1) o,o- U2 - �'. (.·I :I) p.,) (It;) pak /P., = !J,:l y-!1 [/II, (A - I) - :!] � :1 y1 (.-l - :1) ( 1 1;11) oo, \',·""· \' r. l:J je pruste 11,·1>0jnwnov slo. T,·,l_,· i \'�·- t i � l u. n�7x ,. z:-'n·urk1'1ch , · r. IH. I Hu j80 o :-: 1't (· . . li,it-il'lt ktl'ni 11 rl ,i , a j i cc I�- ,I r II h (ka1egurii) j,•, u_ _ l i i . Hnztnl·nui ,·,:l11:·111a .'h 0 •O :--e jC"non1 n1{•ritk 'lll podobrtn:-1 . ,- • 0 20 JOm 1. }' n .I '.' Ia­ ,o j,·clin�· prip,111 c.-1,· knt,·gorir. 20 25 konkreti�ujc t l' t· o:.: c· ho n c :.: e:.:t r o j i n, i ti a I;.i v z orc· z pr ..·. v , . Iil i n y . {· { r,; I a a jt·d n ·l· poj nu• no,·a n ·

p • tp n 23 . -, ;; .., II! ___.'-�--....i ...... ______:.;...... ,_..,.-,..... ____ J______..,_._...,._ _/

!!!l!!!!!m•------ii'..:,· _ 7'__ ._"'""_-- ______Empirick_y_ vzorcc pro vzd·alcnost /• od s t IL v i d I a n e j m c n ii [ h I o u h k y h,.

l• Ucinmc tg ,,1 = IP (22) IL vynesmc v ohr. I :J k i1sc/:knm /' pornclnice tg ,,, z tali. :1, sl. -k l• = /P tg co = cotg II tg

I!). E 111 p i r i c k _,;-. , z o r e c p r u v i· p o i'· c t n e j­ m ,. n .' a h I o II I, k y h,,. Polozrnc (obr. 1). Pro p = I jc tg ;r = t g n ( 17n) .fr/ = = "· -"· p = oo ., tg ;r = 0 ( l ii,) d, - d, . Id tg a = --, - ( 1 :?.,) 1 7. Empi ri okf vzorec pro v_fpocct h louliky 'v\ncscnw-li /• jako ttijcck_,· a Jr/ jako puh1dnic1'. . 11 � 1 , o cl �- 1,3 z t n ,- cl I cm. do,ta1wrno uhdobn_)'• nij[f paprsku odliknS·ch podlc: 1, jako nu obr. I:?. \·yncscmc-li ,. ob,·. I :1 k ,, . t'ck,im p Nazveme !h' - h0 = d3 (ohr. :?): pnk z r. 17 poradnicc: tg n z tnb. 3, sl. :J. obdrume kfh·k u . kt<'ni. = = d, = I• . tg _.., = cotg rt tg :r (J'!h - !l.l (I ) 111,i pro p I tg n u; pro 11 = rn a=0. (;rafiekv · -- - - = v.·�· } , ych1izi max tg n = O·()!lfi., pro P ='= l·l; po<':tiii-sk_,. 1,_,: _ kde D," = cotg ,, tg ;r. d10111 jc zjistili d!'rintcf funkcc poclle p. _Jc/ = /• tg n -� /P I g a tg = I . l, 3 = !11 ( l !ln) 1 ro / max _I /J ,._,·ch,izi i::rafieky ,. r,hr. I :1 pr,, oo . /, 3 = oo ( l !•lt) pro p = /J · 1·:!.irnax 1 /J = tl-lt.,., ( :!t;I,) .ijC'mc-li r. I ,;_ j,· - v_,·jdC'mc-li npet od r. d3 = I• tg .-, a p11ui h, = /,3 I,/ � (�11) _c/3 = :I tg .-,y, [11 (A - 1 ) - �] = /'!fo • ('Olj!(( I!( .? f/'!/e - 11, ) - - l't•l)!,, I)!n t!,! w (11y2 - y1 } - 1, � A - -- :1 tg :r [11 (A - l ,� I) 3 = y, { ( I) = /'!h- c-utj!11 (/'!/, - !I, ) II(! .? - t g n tg r,i) ( :!:) ,., ,, .. I �

1Y I I ro 1 � rz.------�01 I:! II! 01J I:! J- k,- ( :: �d,) 1- {f "':[1-f. ;f,pJ- o:{-f- rA -,J-1)} ::i:· -+---+--·! .... \l C:, 07 � .-H,_ f· ' 1-.2y,\: M , � "ti' ..._ • ,1 A---!-4--'--+--l .._ l --+----,L-�ra; --...... • Cl.),-,. 05 t---t--t---i-- I �,Q.f I � c::, � 0 "'. I:! 0 -} I:! ...lei. -:! -- .. -- " � � �l:i: - 1 .. ::i: I:: C C "' 0 ,�-a-��g��w��" ���� ��--�--s�--6--.- ' =��- �"'I �-- .. .. � ....! ... : ,. Obr. u. ... . psart: Jinak 1.ll..e mll tno [p (.4 - I) - :!) (� ) Jd =/Pig a tg (1J � 3 tg O tg

4 = 11 .,,J) ;1 [1>(.4 - 1 ) - :!][t�:r -'-tj!nt ... h y1 { : (A -1 ) - (:!!I) ...

rne1"11i� rnd ni111 -kokP111 E. Ubytek mt>ehuuieke ym i nrHAlut im- n,dut 1. 1 u 1· 11 11 i k ' ,, 11 ,. r I( i e r ,, 20. b y t e k 111 � c h " u\. ;. n�· ·h hm C nepru > > 1• !I C C <:> <:> 1 (obr :!) � s � � ., � • 1 v pr. ,filu I 11 ...... li pohldnicl'11 , car�· c nc rgi� Je- nwelrn1 i1·k•· ,•1wl)!i1· n111kly u v pro!ilu· II /1 je i byll"k mezi obemu pro!Lly 51 26 27 . �, ·---

(:lO) Cislo b = �B < I vyjadruje pom6r skutecneho (1 byt- n e t y . Uvuzujmc predevMm voclnl R o ku a moze ubytku k k ",:du B. N obr. 14 jo V�tijl rychlost ,,,, jl:i. AC pohyhnjehmota vody f q v pro ­ . � oorohovan6 ru, kres I ena cara, jojiz po- raclruce LJ/J,.P•l = B IlOdle r. :12 a cara LJHP•l podle filu I pfoch,i_1. i postupni' do nu-nill r�·ohlosti t·2, jii'. !le r. 3:J. pohybnje t,H hmota ,· profilu l L. Pfod8tnrnje tcdy horejilf uvahy . z namrta. so taz k a clt'.. !ez, ,ta. teoh­ o , ·2 ]'roudovyo p ­ r 1 z k at ti delku v o d n I k k t . · . · h prsck sc postupne d c f o r m u j ,, pc!llfe b c rl (obr. hoo s o u , J Je, deI ku . D o a. h i Oby se t,m I), tcdy clclc I. 1. tlo11·£ky !Ii 110 tlousCku1'/11·�· y,. Pro � o v6tsihocl ubytkueforma cnfiLJH? O taz' Y zodpovim pozcl6j rl\Z ncprufoyna h hmot, t. j. takOY)'ch. jojicht. dcforma ·' · i . zustava po ni.zu trvali\, platl C ,i r 11 o to,, n ,·()111.: .. z r a o c n a p r ,i c e s I I y t i 'I. e j c r o " 11 a p o­ h y tb o v e e11or g ii pfislu�11c 1. triiccne r ch Iost i". Teto Yet�· uiil Hor cl u pro m/'!i'e11i ubytkuy mechn11icke cncrgit· pi-i rnihlcm 1.i1icn i ncb roz­ 'ffe11i vodniho proudu. - Vyjndhne z1iko11 ('nr11otuv:

=-½- q(r,-l'�f (:11) 1,qB -f 2 (r, - ,.,) B = (:I:!) :? r,

0 11 Ill h II II k C r g i O \' cl f :!I. U h �· t C k m C C i c C 11 e � k o k em pros t �- m. m 1· c h n II i c- tl11 i111 skokn pro,tcm i, h " t ck Pi'i " · B , . r . · e t' 11ergic 11 cdosn hnjc• hodnoty och·oclime-li vz rec , . :11. O tom s,' s11ndno pi·t•svcd ·imc. l' do r. :ll p ri�lu'rni kt.-�· unidi Koz ,. 11 �-.') - Dosadn1 l pro skok prost �- . . yc• itcin�· . l'omdnirc LI jsou ,. obr. 14 prihlcfoniny k (,.- ·ck,im t}· , ,.'J. .,lf,. t. 1/1 = - -l- y,--· - y,. J. k pro . tvm (· f�lum Proto zmei\mc ,·zorcc :i:1 � y :? '.I - tnkto: Z rnn1icc- -kontinuit,: \·y i-1 - + . Jadf-mp '\?· t·1 , 2 Pouiijenw-li ron1itc ko11tinui1.,· . a dosacf,nc· Lio r. :1:1 • , ,!h = r,y, = q .' /1 = ..!f_ (y, - !IY h 1 · I a 11 p -.! " --.:;', =.-.,-=.:...... -i 1 ' ·ch rcnkd pro pro fil� , y,·y, (y, + !J ) a ro,· 10,ti h\ drnulick,· skoku pro,ti'm (,

29 .. : ,.,

Spoj�e: 1h + LIA. - P1/a = _..:tfa; pak . Podosazeni je: • (A· - 3 ) (34) LIB• ::, "1-( � +Ila) (37) · LIB ) = (] - 1 ) (]11 -1 = 9 "1' Pro Jim itu p l, t. j. pro vodni Bkok pl'Ollty = ,i;; = 1 neb jinak, jeito .4 - 1 je podJe r. Illa ,fa 11a - g = a (A - 3 )1 (37a) paJ, - J!L (35) "'AB 6 A -1 -1 Platf tedy pro LIHP-1 rovnice 37!1, 3.'i, 34, 33. pod!� S � f­ rec 35 - ro prosty vodni Bkok odvodil eenn = QC . I = v r. 1924 v Engm g P r o I Im· I . t u p Je O a podl e r. 18b ::"n e z e J/,prve Stevena pl News Record. d8 = O; �- = e v o d­ vi9 • Jh.. Jh.. ]Jfa 3 y me c ha n i c k e n or g i e ted,• ,:JHP•z= k = i 1 ( 7b) 22. l) b t e k °io mt'!- ., I 2g Y 2 prostyin vyji\dteny_v n f m ekokem v profdu I . QC c'hanicke energic H1 Pro p= i!inf ubytek mechanicke energie celou rychlostnf vysku v pro· : 1 1 = 1 Procentnf ubytek etanovfmc takto f i I u I, i!ili v = o a ztracena rychlost v - "• 11 • Kfivky libytku mechanicke energie vztazene na 100 LI B 100 C Y1 16 t•i2 Ullei!kovou 08U M1 a -potadnicovou osu LJHP, jeou vy­ = + krealeny v obr. 14. Tvotf pall omezeny dole knvkou Y1 2 g 1 ----w;- LJHP• , nahofe kf1h-kou LJIJP•z. 1 Kfivka :JiI.. P- , flt'Mtrojena podll' r. :12 zna/lfcf ubytek 25 C 1 n = -:r 1 r, mechanicke energic ze ztrace e rychlosti t•1 - 111, pada 1 = + 2 mezi knvky pro p l ·2 11 p = I-:1. Tc d y ,. z du t f m gYa 3 \' o d ll f h O 8 k o k II JI _;_ · l :?5 cl O 8 & h n e 8 e t Il­ 0 a H 1 2·5 (.4 -- :l) (311) k O V Ch O II b _v t k U JHP j 8 k O pfj r Z U ti!J e dokona I e = 2 + J1.9 · -x=--r- nepru i nS-ch pohy buj fcfch se . · *frant•zo,·t- · r y c h I o R t m i t· 1 • 1•2• Tim je naznal-ena 2 odpov� 1111 TYar 3i; ,·y1.ka j,• .1/ . "' I . l>umrl byl v�·loien ,. Rtudii • .\. •l"I n b \' t e k m e C h 8 n j l" l' e Pro 1 -· · • · ,. o d n I m � k o k •· 111 • Wl<•rku Jf = I ·!I ,-�·kazuji kfivky t�· zmi.lnu kri­ t -s m ,.°"ti. Hotlnolll .J/1 I ·!I byla ,·>-pol-te11a 11a ko11ci od­ i t i v-S·�ku n:r.1111i·,•11i �111 ,·ce run1icl 2. me pro rychlo.•tni \"ZOl't,l' Z Za,·ed' Z«• ;17 1111ppoHieemi, ktf'l'ejHOU zftojmy r. (Jib, �,�,- 1:1. 20. pn•j

SI r - t __,.

hodnotou jedint\rozmt\me 1 "!'':zd111_,, 1�1. l-'m1cv11cl1. pniv,i stn11111 r. 4:1 d,i , jak ji· byti snadno zaml\nt\na jinouvelilHny rovmoo a pf. spoi 1tostktcr6nl. mM.e .d ,· � � : 7, l'CJllln, n . hod11ot 11 kl11d11011, j,, v1.clv· JH• > 1/1. 1. l l,1.,·11•t' ,�\',r 11d11i11 1·,· fl• jl· d,i,111 ron,ici . 1J­ '. ! -1 "f I' \' 1 'I ii �II n.,· ' 'I. r 1'<· t•. : k I c· r G IJ y I y z d u ti II ,. n ergi e\v o d n f m 1 J H' H . 1 11 11 11 0 O 0 11 24.k Uk byte k)m d e chan i ck �z l· J' U p J' N k IJ k \" Z cl 11 I .,·. II k Z j j 1 cl r c n $' v °lo m e­ t.• - ll I \' 0 11 1 II l'- f Z r, 0· s hao e m e v z u t y m " y j a a � u � to n ''I.,· <· k j t· d n c, t st I, filu I , · odn!ho _ . c nick cnergie H v pro j 1'.r",I Ji k > k II \' ti ti t {• h c..� j }) r 8 k O k ll Jl r O R t C h O. s t· I! o. 11 s, , .Y 11� k 111o k1· l :-1\" oO i· j j t· 11 11d 1 ,·. 11 j t 1 n <-·p rt· k r n t· 1 no z k k u \" z d h ,,. 100 .1/i• 200+ . IH• 1 1 + 1 = (2 !,/ ) l I O / :17 doy k y, osadme z r. r. :.l!l I . 1'-k11 · 11tV \'7.nik:i prt·\·o\·· 11•nim t·i \i i' k, - (�; +d ) I. \'odni_ � .\ z,� . . ' ,cdrllu- 1 i111 zakn1 111lt· \•y;iky1 \"t11·.d11i lt11 .. k k pro!- J,_\ 1,, 1 1t11,Znl·nn odn,dit j · \ 1 - � - 4 (A-1 )'+ JJ,• - (·1 1 ) tH \";,, , ...r,·•·� pn, �k k \Zd111\· i pr,,�1 \· a 11k i .. tti ., 2 .Jr � . = _oo J ·d,11,! 11 1,1 ho11 j1•\ 11. \'udni ..k,, k iu·\·zdu1 \· 11,·i _ :.1 _ . L. i . - pr, , ... _.1y J•· J1·1 ,. \ lu ....t ni pd pad d,,l11i 111t·z,· 111in· \ ;,,1 1 i ,- D,• 3 ro,·­ r:r;, n rovnicl· -11 pl-ejdc , 11_ t t 1 1111 Pro limitu p = I. Dl = I 11: /' I ll,,rr,1 rnr·;,. /' da \·;i 1. aji111an·· \: \·.-. l ·dk\· r. -1 1 = O. '" r. 40 d _ · . nici :l li. Pro limitu J' = l�·or,·� 1t·k,· ,1 --\ 1·1 l11jt· j.i ...11 t· rwr!.!•·fi ·k•,11 l ili ·i , ,: 1 - J. I •• Jt•Jto JI'\ II. t. 1 rn I . = 100 ., _ ', 1. · J 11 \, , I. \ �rl11i \ir '1. \4.Hl11rt ,\ 11t· o ... n.id \ ,1 ... 1 1i p1,,11d ·111 ---- 1 11a11--t1 pr· ::- ul• k \'Zktd1111,·r ·- /' .. ,1,. ....111,··111ak 11i od1 ·111 pr1 1fil111 . k prnfil '. .� -oclime puui.itim ron,il·e .1 ktcn'--i.to tYar tnkc snnclno oc\, 1111ro11 .1/ l I 1· 11 11111 .. l t 11\·/·1i r 11 :J ib." orlit i 1 11_ \ n·h l oh11to �·od�1ifi11 \ irll, /•'jlllt•fl,I jll I ,·,-1 .. j ') /'• ' b�,chom mohli od,- ka111_ 1'_11\l_ \11\ t· 1 1,\ ,11 Analytick_,- velmi znjimnn J zrt·JIJlt· h 11ka\111. p1,11t·\ adi. j . p1 ,d• ni vzorcc- dt 1J'I I\ !11°•. f'l1wh,\ ,,t:if·1·ji,·i .., . \1111 \ k,d 011 /fP 1 11 1 11 -- 1 111 1 1 1 fl,J take tnkto: Pro LJH• a pro --- 1 1a a 11 1 1 1 , i . Ii l'1·1. 1tH_ ·t 1 1·h.,1 111i'·h·11i 111 11i. 11ila \ .\1·i l 11 1 ..11, / \; ' Ht\ r111· 1 ali 1 \ 1 k. tlah.y dn1� 'IM" Tifi1·k1, , \;ihu :tl, --p f ('!11 1,l in,· P k, ---'i;--d, _ . 1 _ J f/ Jr .L ;--.p1·1· fu·ka \ 111h 1111111,·1wh \ ud I IllI llll"fl-. 1 . l'IIJI lllt'II.._) 1·1 J11 \ ,I 1 . . · 1 1 nih1. 1 \ir11_ k�, .. 1-\ 11 r11:lidy ,1·l_111i z11.11·11,· 111111 J: J•· Jl/ = Y, - k, - Ye - k• . jt• f'. l-f ._J jt' _1/ 111 hl11.1· J'' 11111frl k pr1 1f. I ' (ul1r :!). 11 Odcctenim obclri.inH': -·1 l.11·11, ,11 \_\ ...h.11 j,· ...1,ra\ 111· l,rat1 1 •n, ,,1 ,Ji J•·\ J . - � ) k ·. . IH• -. If/ = (1 • pr-u \11d11i ...h,1 1k pn, ..,_ \· i \1.d11t_\ 1 11 ,dl,· 1 .-, t "I I'" -,' /. · I '· \ \ .. /, ii jlll.t \ f k1\ n·l1 1 1 \1Hl!11l11 1 '- , _\ .. J...1 \i_ l(I_\ Ii I /;I .. ,.1\ idl,·111 ..0 ,. iLi ,,,,·.-11,· \ _\ JH14'j.. ( 1:l) ., _ 1 h,11 11.1d,k,l· d1w111 l,,,1/Ird,t 1 1. 1 1, 111,\-., ·1\ ,I-... u, h 11/ • · rl\ I \1'1 \ .. J,,.. 0 1 1 j,,111 · · ..,> <: j · ul,_,·t<·k 11w1·h,111i,·k,· . Prava stmna r. -1:l, , j,nlrujc ,,11 llllJ11i/,,,\,•. ,-,·1si. ,w;. j<' iil ,_,·1,·k ,1,.,.1,, energie ,·zdut:,-m skok,•111

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9. Delko. vodnlho �koku je d,inn seM,·ro11a,.oh11011 vyskou vodnU10 skoku; pro ni hyl_v od,·01.c•ny ro,·· n.ice 11 nz 1611. 3 10. Pro vfpocct vj,il.ky \'Ody h zn �tn,·idlt•m. 1wj111l·11�i hloubky h,, jcji vzd1Uen0Rt. /• od Hhtl'itlln a pro sklony povrchu vodniho virn jsm1 odv01.,•11_1· 1. prf­ myoh lllQl'('ll{ t'll1pirickC VZOl'C(' 17 ll7. �ll. c c 0 11. Obytck mechn11ick6c energic pro vodnf �kok prnsty je clan vzo,- i :13 nz 35. v 0/ 1·zor c111 :ui: pro skok f:-JTnE EXPf':lll:\IEXT.\ I.E Ill m:ss.\ l'T 0 vzdnty vzor i 37 11 3 . \' 11 vzorei :l\l ni �:I. xm·(, .. Dingrnmy ,. obr. I� n 1.; d1in1ji i1pln,(• olm11. t•m·r­ getickj•eh bil1111ci :,kolrn prostcho n nd111tlho II jcji<"h vz,i,jcmnf pomcr. = ' l'ar 1•1·1 1(• (• t111lt• 1'1111ll'llf r·o11tin 111• l ctuclt•1 l'x p(·rilll('ll· · ·t . • 12. Pro vzduti p I t:; do,11h11je i1b� . k 111c<"i11111id«'· tnlt· du rc·�s,1111 d'c·xhansst·nu·nt qui a t '·ti· pu hli,·c· <'II energic ·pril·od ·· n�- ,· ·zd11t_, 111 ll·li oclnim ,kok,-111 1 1n:1:1 duw, It· n·<·11t·il ..Tra \'HtlX t·t l·tudc.-f-. de:-- l11:-:tit11t� kost i . ztn\t_,· · ... 1 :! . · . Hoi·do, _, . klt'ru j,· , _, ·j,idh·1111 rt" Xa1iu111111x M1·drolugiq11t• l I llyd rol t'chniquc· T. (;, .\la - nici :l2. \ r. :t2 znuna·mtji r . r rychlo:o:ti vodv • ' . i-.n r\'k. 1 pi-i�luijneho ,·odnrtw skoku pm�tt1ho . .. Z1 ni I u H.. r (A. di ...po:-- il if d '1•xpt'·ri111c·11tat inn l'�l rc·prt•!-,( •1ttl· pa r· la doYa" znaC'i z1\ruvc1, lth_,·tek m '(:hani1·kl· ('lll'l),dt• 1 i. II <·at fur111, · p111· 1111 dPs c·:1111111x ,· il rt·s de 1'111 - n. niknjfci n\zcm t.lokunalc• t1l'pnd11_,1·cl1 :! l(·I,•, ·1•• fig. Ii 111h· :--t·C·t io11 r1·(·lt111�1da irt:·dt• 1 1.70 111 de ha11- h�·bujfcich :-:e zn :o:t hou ryc-hlrn,t mi , . ,· �1 it11t 4 ui u · · utilL· t·i.;t dt· li rn 1 tt.·11r, o .:«.I m dL· largt.·11r: :-:a l1,n,L!tH·11r 0 , 13. Vsecky ,•zorc,· ln-h- oc l1·01.Pn1ho· Ink. ;_,. st· skl,idnji zt· :,colt fond t·:-1 h, wi1.1111t:d. IA· <·t1rntl 1·�t m1111i it �011 (•xt r(• ­ ' . . -. dvou i1odnot : h�·z;ozm,·rnt pro,tt'.•1111 ,·ialn k,,., . rnitl· ,r.1 mo11t d'1111t· \'111111(' (•It ft·r. il :trt't<" i11f(· i·il. lll'l' hi­ . ' -. chanikterisuje celou kntt')(Orii j,·,·u li,iel. 11 ,,. od :-(•autl·t·. En a11Hmt d1· h, va11n(·. !,, .. paroi:-: du canal out scbc jcn mN·itkcm pod, ,hnoM i i. a ik>11w j,·tlirw um· lt nut1·11r dt· I.', II 111. IA·� dt•:--.-.i11:- d�t,,illt·. dL· (·(· diz-'- rozmcrne, t. j. poj menurnnc\ n•lii· iny. jt-jli ,. , hi,1 111 1•0:-itif:-11111 n:pn'·--t·111t·• .., pa r It·-. fit!. 4 C'l .-, dun:- f'(·tud<· hodnot11, stnl:i,nby clokonak· nrcilu kunkrt't n( pfipnd. pr,··c·,�d1·-- 11l1.·. l),111 la pn·111it'·rt· ,'·t wll· 1 '1-111lt·11r n c·.xp/· rimc·nt<'· rh· la U. \'seckv. ,·zor·C'c pro vzdutf ,·,win! skok ph·1·h»z1·ji ,·e \'Zorce pro ,=·odni skok pro,t�·. poloz(nlt'-li , ni,·h fat;on --111\l'c-nt'j.im h�·clmulll'kt.'111 ml 11.cni. \11.'11, tnrr,·ntrn·u � rlt- l'indt.·� . 1 ' • ,1\1 y • ,· .-:.i nifient

0 l,l pr<,fu11d,·11r t·1 la , i1,...... ,. d11 <·our:1111 1 torn.·nt llt·11�. (/ l"HCTt·ll·r.1tiun dt.· la (\t'"'itlllt·11r l.'iwh·.\ J/ ,·-.t 1111 11n111hrl· nh-.t r.1i1 : Bou:-,11w-.t1 ) ';1 ,·m 1l1 ,_, l· •1 •11r r:1r,1t·1t.:ri---l·rt la tor­ 1 1 1 -. n·11111j1.... it t'· du ('flllr.1111 dt· rl',111. L\1ut,·11r a l· l ·,l· Hl'110 · ' fit·i,•lll'lllt.·nt h· 111,t.•a11 dt· l'l a11 i\. 1 ,·,tn 111itt'· d 'aval d11 ('/Ulnl. af111 1111 '1111 l't·----allt d'1·,h,111----t•111t·r1t IIH fll'II l· l1 H1!IH dl' In ,·a un,· ...... pri ,dut--t.· 3b -,,.

-11.·•

' Pour In µrofondcur y1 dt• l cau en n,·nl du n'tlll1mt (voir r c­ In fig. I) ii II conHtate une relation qui ""'t exprimk> par l'ifl1•ntitc\ du Cllrft(•ICrC' I. Ir re:;.,n ut :;c nll't •n 11011,·t•incnt "ort du tnhlC'au � quetcon J><·ut po"'i'r i ....:_ i, i. Les ,11·ers la ,·un.nc. 14·arrctt, pre�1 de In nln1tl' t il N.:' p_rotluit hits ;, t·t ,, - i, 0111 jaugils prcciscmcnt pa.r le tuhc c 1 11 ph(•nomen tpte rnutc1 r11 ppc-llc· ., r,·ssnut noyc·· de· l'itot . Le rl(•liil ·i du tourbillnn1 ,·nri • d'unc scctiou (fig . ,.. Ii. i) eontr le ,.rt• s" .1 11 t no 1 - no�- t' tn111.l"'\'l'rsi1le i, J"n11trc•. la c·n11rht· i dnrn;; la. figure fl en . . d um· I •xcm pit·: i I eroit '"'t·c· I · clc-gre J de 110,·ng , (cloigntl)" ct,, •on et 11 fi tm·s fl l'l IO). n·1'�1ut Clnigne'; apr&:: eda ii a ,'·tahli dt- c·<· n.•,,:,1;u11t nun 1 )! no,·C lt':,i. n..·�..:.nut:-. no,·t'� (•n l\lt vnnt pro1!rC':--,in•t1h·11t I{· 4. L 11 � u r f II ct' d • f (fig. �) rlnclit tourbillon est . . . ' nivcau ch� l 'euu,en aval du n•:-.:-.Hut c·t·:,.t ·t,-dil't' <·n fnj. cvidc·111 11t·nt cunc·H, ,. (fi . .-, . fi. ,. ) pnrce qu ellc fait , ' · sant succ,•ssin·nwnt t, dq.!rt· ti,• no.ni�,· de• I' I it unP . urfaef' cl,• 11i,·(·nt1 dt• l t·a u qui tournc nutour de l'axe hori,.011 la I. II II J) =-e:! .:;, 1 · L s ,·a riatr ion:,i. sl'lon /' pour la 111{·nu· ndt•ur ch.� .\1 :i. Les p r ,. s s i n n s d c I c• a c o t r !' I c o II r1 rl11 can11I nnt i\tc· mPsurc'cs par I !I tube piezo­ font Hl1l' r:.C' ic- dt•:-: C':--:o:ni�. En c•n:-:,.. n1h lt·. 1"1111u•11r a P\.l·­ f .:, 1 cutC ; :--l•rit•:-o d '(•:--:-ini:-: numl·rntt't·s < •Ill frrit,·, ,Ian, It•, ,.,,1, .11,w, < P · , II rnaint i<·nt la nll1·11r'. :: de· l't.:' uation :Jc au�r-:i 11our il•:-­ e t :!. d ta bll•H I. IA·Hr :-:ignifit·Htion n·:-:-.urt th·:- fi�lll"t':'-1 I l· ·a, oil p 1·4 l'I c·alc11ll' )'. rle l '(·q 1111t ion :id. " ourq le . , L :- pri1u:ipa11x n;sllltHt:-t ell' l"t'·uuk du r,·:.:.•,,a ut no_, l; l'l'�,H\11 ll1Jl1·11U_\'t• ii lllC't 1 ;: =: 0 t"l •;t l("lill' }'/ de ('(' 11a ­ e ·· l :--ont IC'$11 :,:ui,·antt•:-- : 1 tion :J li. IA·:- ntll·lll':O: )' )',a' . ;: ain:-ii c-alc;ulel':-- :--ont in­ v · . I. t:a 1 1r11lt'11r a das,:ifit• IP, t•,,-n i, cl'apr,·- It· ,,,.,nhn• . / > rilC'S tla11s I,· talill'HII �- == · ' f't t1 l•:-t lt� rlPµrt; dt" no_ agl' I'· ( t:tll· t·ln:--�ifil·ati1 111 _ . ' l ,; J,. 1w,ids ,p,·<·ifiqm· de- l ca 11 d11 1u11rhillon y, Y:i n rendu po:-::--ihk· l 't;t;.ihli:--:--l·nh.·nt

36 37 --;,- '., .,. j '• '<

e 3 cont1 -itmt le rnhll'IIII �. pour le r sn11t non-noy6 cl . de In 11·1Jfonde11r <111 ·011r1111t ton�·11t1u·11x. 11l(lf">l dans la ,l/ 6.7!1 1•11 kg dm y = 0.:1 1:J i1 l'extremit6 d'11ri1011t 1 • 4 .· ·ct ion I (fig. :?) de sn co11trn·l ion la plus grnndc. du tn11rhillo11 t•t duns lc•ij distances de 10 cmS it 10 0111 / du r,·sHallt 11on-noye en 11v11l OA l-1, n ..i: 14. 0.0:U,.0 U.701. 0.7.,:!, 0. O\l, O.S:2:1, I�. Ln lonJ(11ClLr . P · n.irno. o.SS:!, 0.1100. - �� n genernl le poids spfrifiqu,, de , , L·t·II,• / du 1 ,·s>-1111t no_,•(\ (figr. I. :!. s, 11) L·St Hi.x-foix e . l"c1111 du to11rhillo11 est d ><11tnnt plus pctit qu1 I,• rl<'gru pine gn111de '1"" lu hn111,·11r rlu rl'se11111 . !h - !h <'-t11nt i 'IJl1t de no�·11g1• csl plus pd it. que Ill nombr .A1 est pluH In h11 11t1·11r du 11•ssu 111 11,m-110. c L·1 JJ.th - !h et1111t la < C i, grnnd et que In sN·t ion t'n quest ion est plus proohc de hn11tc11r rl11 rt'S>-11111 nn_v< . Les lo11gt1L'lll"S /. [P rlc- ' 1"nni11l' fi pnr !Ps (·1p111t ions du II lfJa. l cxtri• mit, d"11111011t du tourhillon. 0 7. Ln h1111tr11r de charge de l'6co11lc­ 1:1. )A'S poirls ,p�eifiq,ws dc- l'ea u d11 ·tnu rhillon. !C's r c . m e II t SOUS1 3 In \" 11 II II C con�idcrcc COllllllt' In dif­ pn:•!<.sionH : 1t•l• It•, d(•hil, i Cl/1111 \' rtriablcs d'aprCS le ffrcnc-c /, P - /, (,·oi- In fig. � ct S <'t l"eq1111tio11 .i ) 1- atc no111bre .ft/ It• d,·gr,· /' dt· n•>.rngt· ·t la distance d ·a pres l<'s r('s11lt11ts rlc-s <'sAAis la memc· pour le rcs! < de- y4• :. y. 11. l.,l pt·rt1 · dt· <· lt aru-1· du,· au1/ r,/ - ...... n11·t I I. Pour tout,•s lcs grantl,·111-s c·alc11lccs c·i-u pr,·, 1"1111 · 11 011·1111,,1 ·. t· ·, ... i, d1n·· I., d1ff,·1,·111·1· ,·11tn· la tcur clcd11it toujoursI\ a111\1ssi 11nl' for11111lt: qui n ·,·�t com­ , H TI I'. CO 11 l' l' . ha11H·11r Ji du pL111 d,· 1'11,,q.!t' H1t-d, ....u ... du f1111d du po-ee q11l' cl ll 11 t, l1 r CY1· A b St r II i l ct d II n I' 11011 11· d11 <.·,lftal d,11, ... In ....,- ,·111,11 / ,, )". ,1n·r11i1,11·· d ',1 111n11t d11 rt· ..:--.i ut gr cl C' \I 1' e, t icrnifiant ll' 111ininn1111 !h :-- J11•) 1· lft!! I) ,. t·n t·t·llt· l/ plan d,· ,.:harµt· 38

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,,

> 0

clans la Ht-ct ion 11 II son < Xfl'l'm ittl 1cl 11\'nl. rHt donntlcp,�r It's formulcs de :1:1 A :i:;: t·n • 0 dt• H INlr In formule :1t1. l..a formulc :10 a t'.• lt> dl- p I non-nn_,·e) jus4u'1\ In limit<' /J ' oc. Dun• lo figur 14 tll' "nnt r prt'"'-'111&·� qu< Ii,, 11t·rte, de cfrnrge d,·$ groupt' hit q et qui nnt l'l>temh1t• du 110111hrt• M, e jusqu IO· !l!t, duns In figure t.i """' r- pn\f;(1'ntt s c·l'llt's de ton les groupc. nlors ju:squ'nu 110111br .'11 - to· :,,.,7 . W. Pour In rnleur du nornhrc .If, ""' 1-!J on n,it duns le� figt1r<"s 14 et In I"inn•f'>'iun rl,· 111 ('11urhurt' de ljgne,. L'nut,e,ur cxplique et•ttc i11v�r1;:iun par l 'annly:-W du <·h1111- gement du eocffici,·ut d,• l"t;c,mlt·ment1 = sous l "nrel,• vin, d!' la ,·annc ct calcule la rnleur Jf I.II d• l"tlquntiun � c - 17. J.>our le "degre I' == 1.2,'l dt· nuyage. la J">t·rtc d • I chnrge due n II r ss;rnt no�·c e t ct •ale /1 lu pcrtc de Uorda ex.prime<> pur I"equation :J�. t·, etnnt In \"itesse ('II 11munt . ,·, en an1l du rc':;,H1t 11011-noyc\ rcsiw tif. I . Le res&1ut noyt' r�t un phenomknl' fo11dat11<'nt11I pour la d6tcrminatio11 r11tionndlc�I!' la profondeur l'I de­

la longueur d'un bn- in d'amortissementc dt•s hnrrng,•s. Les essais execut-cs par l'nut-·ur ont une tltcndu,· qui -peutsatisfa iretoutc l'exigeanc de la prntiquc hydra11- lique, car le nombreJf, pour l'eat1 - �·ecoulant d"1111 e barrage par devel'S<'a mcnt 011 sous la ,111uw - >1ttt' jnt 1,·a ,aleurs de 3 5. pour !es grunds barrages r lll'" clc· it. 15; pour la profondeur du ha in d'amo11ii<.."t' ntl'nta J'nu­ teurconsid er-e les Ynle11rs du noyagc p ck l ·2 I ·4 m­ me sati. fai antrs. U.S.B.R. Translation - 170: Two instances where the rational theory of below dam sections was used, by Jan Smetana. Reprints from national. periodicals, reports of regular technical duties, 193',. Trans­ lated from the . Czech by A. D. Kalal , 1937

.Part of Hydraulic Lab oratory Report-106

i ,.------�- ·, ..,

1. . T�n ra tional theory of below dam secttons was enll�htned St ate lnet1tut 1on of Hydrolo�y and Hydrotechntcs of by two orel il'll nary ex�r111ontal et.udtc,s of ola 1n 11m'I e·noll•n hy·jrr. .Jl1c �.G.�asaryk ln Prague

jump: whose or tnc1 oale were briefly expt11�ned 1n the descrtpt. ion

or the reBolv1ng or the below barrier of �he water !"'Eervlor at Dtrector-Doc. En�.Dr.JAN SWETNA Hua tnec.

No . )4 Note l. Re ports ot Re11ula r Technical ll'ork tn the year 19?13 No.2·, .::ooyboolr Nos. 2, 3, 4·, and 12 , 19�·4 ,

co oyuoolt No. 13.

In Sni::tnm-- -,.. .o.! ...!:_hes e oarai:'raohs llre -nentioned the pr tn­ Doc.EnF ,Cr.J ,n C�etna

c1�e11 ror measuring or the helow dam e,ec tion e t1lt\rit · ooole in

SpytihncJvi on -�v a Rlver. Accomoanytnp t'i,,Ee are enlight ned T'.�O I ·sTANC?.:S \VHF.RE TrlE f'v< TIONAL ".''ir..0RY OF f1r.L()'S DA>! -;,;e;1ro 6 some further important torme relat ive to the de pth and le n�th of

the below dam eectlone ae the ta� of a e1nalft ,laec tficat1on of the

dangerousness of every below darn section. Fur•�or it 1e �arned to

uee oos ttive c9,;.•e , whtch ts necessary for tho rn� n\ pul&.t to · or c Re ortn s from �a lanat �er lodtcalr Re oo. !� cf Re�ulbr Tt1chn lcal ��t �es

:n f;ect1on B le eho·N n e eoeclat for . of movement of water

in a below da'll Aect ton at he . out fl ow uii

flow occur£ below the eur race of the lower wa •er, ·:e, re are ;tv n

reasons of these c� rt�tn manife a tons nC CerlveJ conP rue ive Jrunol&. cd hy A, D. �al�:

conc1u£1 1one. alatertal fo r Sectton B wee ace utred oertLy ro � 'l. -� ­

"OlV1np: of " ,, ,c' el of a below rl!''ll eect '.on ��l 111111 '>:):Jl :n Hl •i olre

on the Vl tava R1ver, an� ORrtly �ro·o the obe Brva ton :,� •ctual ou -

flow of ,r nte r under a StonGy p:nte of a dam 1n r;ymr..i::-c.e on • ht! Slb\l

Pr l:.tod _v ur. ;;1. '-1 6prP and Son °, ?re.aue

A. Thi, dam in Soytthnev l on he l!-.irava '-·,e right r n�e �� The center f\el d o �er �11s ln th!P 1nEt&

1 of the two cldA f 1eldE t; : -· J- ,.,' .:> t,1od .nte, which ,· ervei; at the ea,ne t tme the on l m . of lenp:t'1, ·wherea e for each c·ut l 1 loc,;1 r, avl11at�cn ar- 11 oart o" a ni-o •ect f'.:lr s:na-:..1 ve,,�ole i n (Ft p: . 2) the tract of Ot rolrov l ce-'lodon�n . .3r,�<. de P-:e ·Jro 1.ict !h(! !"" h a darn III.The cent"r valve ts fully 1ay.,d c!o:m; and "he throu11h , of • �l,;lda (or b9.yEJ of '.') -n. tore .,1th ::>ll lars 3 �:J m .•tJt> . The n ow overfalle 1n the center f1i,ld , nr,c! ovnr n, e s 1de f1eld1.1 the.re , r11c"rJ1,e .:>� ·'-,, t"re: ',Jl ' ·f t'1e O.ll1: \6 at an nlttvation .of 177.?8 le no .ater at 9.11 . The e-:,eclf1c over!'i-lltnp d1scha rpe t:· !'u· a 1n , 3 1 1 .S hut at a difference of level .J " / · 1 " 1 {F\11.�) 1,e . :!".!"6Ctly 1n 11ne wtV, t he bot to1. 2ch rt-,}d ta closed by a::; :3tonoy 111.tc with a re&-ulat l )r, Flo·Jli:p- valve. If t. he valve tb fi. l ly of wat. e r ·..1nder •he .at e The hydraulic cu1ettn11 by :) llt fl ow :e re.ul11rle v,,1 cf .-atcr !lt an elevation of curs tha will ;if triefnes e , a£ thlb o�t fl �a oc we do not hind er to l'l";..j_, _ r.�v, thli; H '.:: ::>;, d":le t.:, �looJ ELn·, 1:-rl,:rate !he land 1Y- I'll . �O and ,, o ·wtt�, 11 lee,.�1 !'A ll; with the u;>pe r level at elevat ion 1n11 on "he r1Fht b'ln1{ ::i" ,._,. Ja:::irAva R:\er· ab1ve Old Town. ;··tth a favorable. 1' "iP >,ydraul le q.ilettne, and for tho ct ress �elow d"me ts raleec! •r n}v e t he ,v at "' r l� rfi tsed to ltu r, �'7'1Att elt:va�'"r 122.:n ' _I · ":'7 wtth fu ll J:'8ls tni>' <..f t he da'.11 , d oes a t the hiFheet d techa r;7e 1S-<' e,� thls onl1 fc!" t• e UPe or lrr ..�3 : lon of rne11j�p l�nd on the left litary below da'.11 Fecttcn , only ls not 1n4 1cat� any dan�e r fo r a so ban.- J� the M'.lrava :=:::tv'lr near To o-,l an. N!lvti:ratton should be ..:arr!ed n1:w ::if the ::i11111rs on the s 1 dP.B , by ·irp:ed a orevent.lon or an unc!erm1 on uo to a .re9.•_e!" thrciu11h flow ,J f water o" ;lo,, • The :no ll•tor,lng rd­ e olan -� nc! el evat lon we hav .. 111·,e11 accJ t"le he avy aide throw , whos by ''"e surr�ud tn11 wat ere e'1ould be a cco�ollEhed by a thr� J fh fl ow of 1nvest,111attone . "i np: t::, the results of our H,?�:',: . From t.hes "' r.Jnd1tl Jne le p-lven t'ie hyd ra u ltc qu1eti nF in

h�l �� da'.11 �ecttons tn the overr�11 o! wat er from the h1pher lcwr1 To atd the clearnes s of the explana�tor. we nretiuo!)()ee at thb eievatton of 132.9� . tha_t the below dam section wa ::- as 1n Fil'. l and we tnvestl.ra te how

the hyc! r1&ul1c qu1c:t1np: eat1s f 1 ee the deot.h ,, r,c! lenp;th of the be low I. ".'hrouirh flow , �o ts obt� lned w1t'1 U1 e ove rfqll from ·a am sectlon. all thre e fields Wlth the same ooe111nir of the re FUla t tnp; va 1,,�F ; so Jn 1 m . of length of the overfall d by a eoec1f1c d1echa r 11e ls th. e ooec t f le dis charge = :J.JJ 5.�··· Hydraul ic qutettng ls cha ra cterize 'l ; "'.'he dt ffer · ne e e 'hetweon t. he uo0t1r ,,r.d lower ·,·ate el f, : J.0 1- ,,,; p:1ven mob1 11ty , i . . tbe oro- r lev s 1s and a d1.t'ference of levels .I and t s f ·f-' , (Hg . l) 1 'r ):1 -- ;-c., 1 ' ·, anc! veloc i t y · 1�::- .- 1 duct of the s,.,b st.anc ee I'?'//= . 1 , measured II. The throuirh flow 1s obta ined �1th the ove rfall e o �h�n 1 turbulent etrAa :n; './1 tS 1nd 1Cl\te deoth and velocity o � a . the I cent.er valve ls ol aced tn lte lowes t oos lt 'on and the two slde y -1nto the lows r lc-vel . at the entrance of t.t,e ::,verfaU. 1 nF ra valves are ad .lusted so •1• I& t ti--e· e 1evatton of the level i� he ld at

o .I Tha numerical table (a) oresents 1n tns tanlle III the l".reat­ l �?. , very ca refu 1ly . Th e dtff erence or 'le-th levels ls A· .- es t hydraul tc qutet1"1� or the P'reatest m.)b111ty :3:l l?St. The symbol

-.-,,,. ------7 • ·I , -,r .,. • , .q ,� . 5. ._} 1'1 or turb11lenco )7Z,:. man1fe�t" 1tsel f 1>t bll throe 1nat&ncea or the err•ct1ve length or the below dam aectlon. Th• f"ii"J- .Z� . We na119 1, ,.. , en�e greater ·�an 3:(1 tts 17reat�rt. value 2. '536 gives tmme ::ilat'llY length ,J (F1(.t. 1, 2, '5) depends on the form or the ove rra11 1ng. e111'­ the lnata,re !�I. face; on the overfall height 0 , an:1 on t.he difference of the sur­ faces/., • Th� e enables ua to fix eaei11 by a known computntlon ror 1:r we substitute. in the olace or the e1ootng ray 1nt.o the

an overfall over a sharo edged weir; and clos ely for overfalls over lower level to t.he bottom of the ettlUn!' oool . (Ftp:e . 1, 2, 3) and a wide crown. The whole dlB tancei, below dams 18 then ,£= ,e- +./, arr�nge from the iziven d' ola1n hydraul ic jump. The deoth o! the r1ver etr�am behtnd the hyd raul ic jumo 1& If we arrange the e!'f'ectlve length b ow da11111, with the J: length of the pl&in hyd raul ic jump J then rl, = T• From the numer­ Set- c0py Pa(le 6 ical table we see that , has for the instance III both the great­

est hydraul ic qu1.et!.ng and the least values , ar.d 1� /1U � (1_

Soe copy Pa �e _ 6 The da!:}_6�I'?u�es e or the be low dam eect \ons may be beet characteri zed for 1 ts dep��d lenp:th by the letters wand ' -f.We accom'l8nying this 01&.tn hyd raulic juop hae the h�� fht ind tcate the relat ive deoth of' below dA.m sect tone ae /' , and tho rel - See CCJOY Page 6 at lv e length ae ,, . Both 11.:ant \ t les - n and 1., are best invest1gat.ed

for the1r izre,'\tes t value11 , 1.e. +. he most dangerous hyd raultc qu1et1.ng. &n� length

Page 6 As "NRB �1ven 1n a orev lous wor� 6t ts found bet neen t!ie 5cc co PY of the 3t1l ling Po Ol 11M1ts o! /, J._ t) / . . r.For overfall of wat er into below -1e·m sections In all three of he Ftven ins tanc e s, tnE bo t to..-. ' I , which we it is pose 1 ble to have for thll t 1me be 1ng , the relat1 ve s 1ze of length :s bol o,: the level of t"ie lower water o the n.:i oth S w ob ta.in ln t h·e et n _;_ �ng /'. o to /. I · as comoletly ful fllled. r.... m e ' the effect 1 v e ceoth -o e l o·., d ame '. o e f he cv.- o11en hy- oool , , , :;l at, hy 'raullc ju11 0 by the meas ur'l of / From our comoleted tests we obtain the formulae for the f 1 - � c. ri.ul '.c ium ,. qffac: �np an ov,:r tobo11-lF -/- .• effect tve depth uf below d'lns and the effective l&ngthf, ,thusly: . 3y th l :u:la tt 11P-y b" Fe n th"\t. t>,e :neli.1ure of swollen f 'hr3u us ed 1nst.. 1; ces ; See cooy Pages 8 and 9 for the tnetance ::a. :II 1 1! the emalleB t o the . . I, - Al most on the lower limit of' : · ,, . ,·c, we have obt ained the

dimens ions bel ow the �ate in the reservtor at Hus tnec , wliere as the ay •. he Ftfe . '1. , ?, 3 we m1>y Bde that th,' :rans format !on , , I ,J. greatest hydraul ic quiet inp- we tool< a discharge of ir, 1 "-Iw hich orren •. i,.l atrea:n tn • re r1ve r ti ream oc (:urc 1n tr.e length of he hydr&.ullC!t.lly iB ooestble, but whtcli was not , u:i 111 now cons ide red • ,;:.

.J ,; • r ._. � i • .. '5 • i: � . 7 . '• =- reae tble under these conc 1t1ons , and w�1oh ehoul� not ever ?:cur 1n 1t would have a devastPt1nF effect on t ne oottom of tne below dam the future below �t.e F'• te , as the re eervtor 1s built f:>r this ;".11:rpos e aect1on. . For ove·rtoo-, 1 nir or "or the s 1ze of the relat tve d e pths , for th1s 1n­ lt 11 then POestble to conclude etance thel'3 were also ui: ed values of the lower 11m1t, 1.e. /. c '· { 1 . 1:very below dam at1.ll tn;r pool 1e comprehPnded and oe.,t How clea rl y •he re&.ctt:>n aff"!cts t h:, t.ottom of the below c�a.ractertzed on the premise of t'"te ra t1ona1 the.,ry of two q 1 1anttt1es : �am s ection from th-, f, 1vP.n two v alues / and ,, , 1s ev !dent from the ...,1 at1ve stze or cieptn, anr:r.ed eant! b:>ttoms of o11ode1s pools dangerousn�s� d1mens 1 ons . of tho dRm tn Soyt 1hnev 1 arran�ed tn •he ecale of By the de- n 2. It 1e t41 ". he ouroose so that the manipJl&.t.� F or::eI' �v::- format 1on w:,s lleaa;ured tt'oe stze o" the eros 1ve r;trength :,f the water

f1 owtnF. nway rro:i. .• he below da1! sect1·in.

Teet s with tt.e ove rfall of wst. er r.e !-:avo conducted for om1c .lly "or dt11ens� oninF o f th-, telow dam sectt'-,n , f''":> .! ·'-r tc ....om each ou1ot 1nia: f.Jr 2 hour.:i and l'.' :n1nut <>E , wh1ch 1s a c�-:;,arttive ln­ part nf t'1P bwJ ow darn ePot. 1011 r.o:Jl� n,1t �., na -.:it,c,:1_yce vau t ated. terval t o 12 hou rs tn the actual Btze. ri-.e re l1ttfwas •!-:en :ih oto­

p:rA oh'.t : es the c ond\+ �:>n neared �tabtltty , 1.e. s fo:-"!l r°".�ch_Gas n.;t _ cha'n17ed fJr•.l"ar ":.y �he effe.�t of t!": e .:•.ra�:n .J f \:.:�".,,r. F1g. '• Fives 7'1. '.

iu ge 10 e c our e t :!..6'' '" for 1netanc " !II.

/- - deno�es t"l.. """'�le length of the t"- elow ·11.::i .. ., �• • ... , Thie then denotee the F !"eatest h�draul ic :i··tetL1i; cf the · {,, �en:>• ec ".he ,._,. ,p-ht of ove rfall ar,ove aurf�.:.· -· � '. •·() least va:;es of r., lat \ve 1�nFt"i "- "� •el,t 1ve depth for a F1ven below ·

dam sect1.-.n. To thcc.e leas t ,.,nu�s- 1s res -:,ons 1ble the e:re'lteet def­

ormatton· �f •he bot.t�m, 1.e. The ,reatest eros ive etren,th.

The hydreul 1c qu1et1ne: or II and I!! are easily ooss l•1b Tt-9se f:,r-:1r.1l&.e rt•re fo1· 1nst�nc'!I l of the dr,.n tn Soyt".h- to 1bte.1n, be.caus il .:1,;moar1t1ve d1scharp:ee ob• a tned by the same meas­ nev1, u rotmentl!I across the �ate of all throe f\elds. l t 1B ve � noneeRary &es c.:,a; P11J""e 10 not to change tbe \ower1ng or a v•l ve o f any one field rapidly , 'as With v1, sot �teur.,.e 1<' rorranf':ed our useful l&l'\ft h �or S;,yt 1hnP.v1, ··-

.,. __ _ .... ' �-...... 1, •"s' . t: • -,,. ;, !1, .· 9 .

fall to tbe l»ttom. It s�uld move th n �ralatantly hor1z oBti.lly. e i These formulae ho'-\'ever for t '1e re sa:--,-.�r -.r:Hue 1:1ec -� J:.ilC: From tbla, thl'.t tbe ray ln ·,18• 7 and 8 d"ea not mul.'a pt•,e horizontally, but ln a curve upward, we might conoh14e that under·

e 1'8 f b -� ,rl'llater potential th ray la ilJ 9reasu. , whlch manifes ts 1 tePl y Se"l copy he_lght. T hle namely 11!1 trte4 fo r the .\nstanoe lllustraied 1n F18. 7 whlob baa a symbol of torrentneee ., 1> J. 1.-,- 8 ,The stream illus-

trated ii. F1g. 8 baa near the ES te a symbol or torrentneBB ; J/ :: I, 1 We obta1n tn-�n oi. �ila suopastt1un ·:l f t'111 rattcr'ul !!1aor-J tat ls ;qultt -los.; .8). tio H 1s seen that 1n a further 'idvance of the stream, this symbol st' l1 �•creases , so lt baa a wavy au�face

Wh1o�__u--a11iiya d1�3�vered when the stream a�proa���� the form or �. If +'io?"II! occurs ar <1 • .:.,n -J r :: �•0 r 'Jn��� t�� pqtA tC'-- y a cr1t1cal stream. (vt z. Fig. 7 tn Stud A low the eu:-f>.1ce o!' +i,.., lci·n'!r wat�r, 1.t may b'! st1t•.ac.! t'i'it the r11y

If the ray !!lll s to he ·,nttom �t may be f:,r two reasons .

1. Either the center has not a soec1f1c weight of / { ·,,, :b•Jt

1• leaG. It has been shown tn stldt•• or swollen hyd1'111,:.il1c jump, that the si;>ec1f1c w4lght of a mixture of wa ter nnd atr for� a whirl - , pool above the ray , can bit percepttbny loJe than / t ,.,·. It was s���!\ that the specific we1�ht was leee as was lees the measure or )J the OVl'rtopp1nr / ' and ee W'!e l!'re�ter the sy'Tlb:J1 :,!' t.:,rrffntness ?

Be cause with t.he 1,rtven dts:ll)s:t�:ln of tho d,i,i Wd cannot ':lave an influence on the sy·nbol or t:>rl"t'r.'ne se we make use of this

' ...... so tbat •• may obt11 1n 1n Flfl'•. "P ft!\d 8 t.he •l'tlced "="" down t. u ·he �otto'TI of t�e attl, 1.nll'. :-ocil of , "it> l! f the cttlH:111' 00,1 . thn 11e n�,ire o � •he swollen scoured for11 of the be low dam section, ae is shown ln draw­ tnir 111 F1F, 9 and 10 • •r, thl'Be ·.! raa tnl"B �he .:-•1r'.""! nttJ are ;;hewn a.;; �- ·.:' z- j'

!"! !. - .:,; � •. :

L_ I'! C _y r • ; ...... 10 ..' f·.111 �tab1\tty. The 1netan'°11 tn Ft1t. Q and l·J ill muc>i nearer f,r th�

n:1.:; :� J,:'.lt· :.�J .

�·.:-e 11d . I!'11e ol ace •_ >:e ;,a.te so �l-r. •_ 1ts e e at1r.;:- °:'er .11. :::, ;,- :.

------

-.- _,.. ' ,,

Statni ustavy hydrologicky a hydrotechnlcky T.G. Masaryka V Praze-Podbabe.­ lnstiluts hydrologic1ue et hydrotechnique T. C. Masaryk de la llepubliquc Tchecoslovaque a Praha-Podbaba.

Prednosta- Dlrecteur: Doc. Ing. Dr. JAN SMETA NA.

Cislo - o . PR/\CE.A STUD IE. q. :rravau:\. et udes.ct

Doc. Inµ. Dr. JAN SMLTA NA: OVA PRIKLADY UZITI RATIONELNy 'I TEORIE. PODJy ' EZI.

Dem, exemples de !'applicationI de la tcorie rationelle du bassin I d'amortissement. (Avec un e:\.trait en franc;:ais.)

z vlitslni otisk z casopisu .ZPH \ \''l V[llE.J�t SLL'ZHY TE.CH�ICKI:.", (roe. t 93.5).

S I:)obr. v lex/11. Al'ec IJ fig. en lexle.

193.5. :\",\KI.ADl'. �1 \" L\ST.'\1.\1. -TISI.EM llrn ED. CHI.Gil \ A SY.'\,\,. PRAZE. -----�-. -_--.: .-. --,.---,-----=-.------�-� " ,j·

R11tio111•)11i tt•orit• pl>fljt•,d hyla os\'l-tll'rm d\'{•ma pft•d­ ehozimi 1•,q1ninwntiilnf111i studil'mi o \'tulnim skok11 pro­ sti•m a nd11trm : i•1i z,isndy hyly stnrl'nl· vyslo,·,·ny pri popisu h-i'a.•nl podlmizi \'Of)ni ruidrz,• 11 H11si111·P.1) ,. {· ,i � t i A tohotu <"·lii11k11 j:--1,u zntinl·ni• z,i:--ady 11Zi� ty pro ,·.,·111H,•11i pod j,. z i z d y ma d I a ,. ,, S p �-- 1 i h n ; . vi na i"P<'P )lnr-:ivi·. Pfi torn ji-;ou ohja:-:nt·n,· n{•klt.'ri· dalsi duJ,,ziti· pojmv: rPlatinti \'l•likost hlo11hk�· 11 r<'lativni \'t•likosl d,',Jky ,;,uljr·zi jako z,iklad j,,d11ot 11i· klasifika,·t· l>t•7,JH·,·ru"t i kazdi•ho prnljl'Zi. Diil,• j,• upozor- 11{•110 na jistou opa t r110:-:t . ktert'• je tft>lm pi'i nwnipul:wi pohyhliv�·m j1•z1•111. \' {· ,i s t i H j,· 11k,iz,in Z\'histni zp11soh pohylnr n,dy ,. p11dj1·zi ph v,\'-t11k11 pod stavi,11,•m . dt•je-li st• \'�·tok pod hluclinou dolni vrnly. ,J�ou ud,iny pfii'-inyt ohoto z,·l.i;.1 � n•h11 zj,•,·11 a odvoZf'll\" konstruktin,i dusl,·dk,·. �latf'ri,il k ,··,ist i B hyl �isk,111 ],·rlr,ak mrnlt•lovfm f-t,;;.,;,,111 pod­ i •· z i z d y mad I a ,. H I 11 1, o k ,·, 1111 Vita,·(·. j,·dnak 111 1;,oo1·0,·,i11i111 :-k11t1•(·nt'•ho ,·.\·t ok11 ,·ody pod �torn•yovj-111 :--ta,·idlPfll jt•z.11 ,. x_,· 111 h11r<·e Ila La hi .

.-\. ,J t' z ,. 1· fii p y t i h II l· vi na h·t.·t• Jfon1,·I· pro­ j,·ktuj,• z,·m�k�- ,· ,h,d ,. Brni·. :',;adjt'Zl'lll orlhuN po pra ­ ,·i·rn hh·hu l.ci \"lalio,·\· wi h1111 kt,·r\· nui :,,;)ouZiti 1.;iro,·pf1 . . ..malt ',•· 111 i:-;t 11i pla,·I·,,.. jako l";i�t J;rojt·kt11 pro ..ma lo11 . plad,11 \" trati Otrokovi1·1· Hrnlonin . l'od (,, proj,•kt11 rn.i jt•z :, polt• po :!O Ill :--\"NJo:,;.f i :,;. pilifi :,-.-, II 111 �irok�·mi. Hrh,·t prah11 jc·1.11 jc• na kott· I 77·:!s. t.j. pi"irnov t'J J"1 1\"11i ch111. ,Jt ·duot li\';i polt• hrndi �tom·yo\'a :.:ta\'i«lla �., :--klop­ """ rt')£1lla,·11i klapkon. J,·-li klapka 1ipl11i· sklot•·na . \'Zdou\'ci v)a:,,;fni tal111lt• \'rnl11 do kot ,. I :•·d · :,o. Ti111to vztlutirn trni J._\·ti lllllOZfll·na pla,·ha ll Za,·laha pc1ZPJ11k11 1.-ii..id, na pra ,·,·m lii'i·h11 h·ky .\lO)'at;r nad :-tar.,· 111 .\ li·­ :--t ,·111. \"1.tyl·,·111111 kla pkou �,· \'Zclouri VO

3/H, t. j. q = 4·2.i m3 na levem btehu Moravy u Topoian. Pln,·hn ma hyt i pro­ pHpnclll kfi m /H na I m rlclky kdc?.­ to post rannfmi poli toliko q = :!·Hi m3/s (obr. 2j. vozovann at. do prl\toku vody nejvyilc :!00 m•/" ZA1'11,­ · HI. Stl'l'dnf kl1tpk1t jc (1pl11e sklopcna ; prutok cinf pri,­ hy oknlovymi vodnmi maj( Ill' dlti o

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Ill h pad nejvt'.\tsl ydraulicke ,.o tifoni Nii nejvNlilhyhnoRt Podlc· t.,d,ulkyjl' ruim ., p vz·dutr 1 l 1 1 ..:_c vil<·<:lr tri 11 _:_ 1 •·j111t·11�f a2·s5 t. Znnk bystfinnosti M = v i<'Vi St' u vkoh · 11,· zuvnn.<-clr Jlripll�;:;� 1;; / "1./� V g Y, Pod h· obr. I . :!. :1 , ·idiuw ,.. fl. . . . pro11d11 , r1• 1111 , tfi pi'lpndt\ o n&:o vet'! nd jrho nrj,·Miii ho ' , I) Zl l \'I�· f nu tv 1k /J (11lu· Promit,ncme svial<• rniRlo vniku pfepnclo\'l'hu l"'I ,-,.ku u,-u pf-c·piul,,,·c'· Juc h\ 1 1; --; • ; , -.i,,,. 11i1 p · J.· ·. 'prc p11(I 0\ (' do clolnl hlacliny nn dno spndixte (ohr. I. :!. n troj ­ ·.,· I, n a rnzd. f111 11 1•.u 1111· ", · · 11n i,:,, 11r,··111 zwim_\• 111 ,·\· . me ,. dnnych y, . • l/1 ,·odni kok prost:i·- Mln11hkn:I) ricnihu . proudu 1.11 n,dnim skokem jt•

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pri trnn , nd n i ,k,,k prn.-.1 y 1111\ , _\ .:.ku ,,, .. (. I :q " d,•lk11 lo ., :1 y, (. I :1). y dnn\·< ·h t n.·<·h prip.ult·t·h.. �t· , th dnn ,p;1d1.... 1i • p11d Ida .'11 ditll1l1 °d o (1ti \ uch \ hlt1t11w!11 l' }', ktt'f\1\1 j111t·1tlljt'lllt' 11 ,·, I It 1 tl PU hl,)11hk ·, u p ndj,· 1.i Tt·d., \1tl11t1\ ;i1111· \t• ..p 1 r11;.1 i ,•oc:1111 ..h,, ,k pro ....1_ ,·. rnirou /' ,1cl111i. ,·iii pri-,_, ... ,·111111 )'

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1m1n = i (A = 1 L1mu O·S.;!!J 1 (A - :1) 2 4 Y1 (A - 3) I k I ' I k YIo u bk>' u " re­ · · p I atI ivn I v c Iik o st� I h L L = l I .3y 3) = :1 :l Y (A - :1) l e e I? 0 J e z Oho 111 r � ,, n v e i o s t � __....--;l'omM- na dolejsl mez n = 0·80 jsme dimensovoli mt \. · vyiiethtl pro nc vHsl, t. J · ncinc­ 3 vee 11,elny _••, p i trebo. J pf. podlmizl nAdrfo v Husinci, jezto jnko ncjv6tsl 7.Vat lz·.en I z klln6jal h drouhcke . b p y llOlld(­ hydrn ulicko zntli.<•nJ _i8mc vzoli prutok 210 m /s, ktery " i lOO predchozlch pruei(•h, eJo z b (o udl\Vl nM hy

Ohr. 7. 1· m o cl I 11 j e z u ,. c S p y t i h n c· v i "cst rojcneho ,. 111l'fit ku I : :m. Tc·mitn rh·fnrrnacl'mi mc·rimc velikost zh�·lc ,·rnsi,·ni sily ,·ody odtckajici z po1 cljczi. Pok11s�· s pfopndc·m ,·od,· jsrnr ko1 11li pro knzclt'.· za ­ ti.i. t•11{ po :! hod. I:!min .. cnZ udpo,·irl:i trvllni pffr-.h1�­ nd1n zatfi.l·ni \'L' sk11t<·<·nost i 12 hocl. Hclirf. tok jak b,·I po tCto doh{· f11t.' ografov,·1n. �<· bli:i.i :--tan1 SC't_r,·nlCn1i1:,..p, t. j. i-.tan1. ktt. r_\' dal:=:im pu�nlwnfm proI. urlici vocly ji;. m·1n{· ni. Ohr. � ucl:in'i prn ,.a liil'ni 1ll'jvNsf ,·fmol 1·11.-, 111 ; ohr. :; pro II l ·H,� 111; ohr. G pro HI :?·.ii m. Odpoddnji 1,·d,· nl'j,·dsinrn h_vclr1111li1·kt'11111 zntifrni 1u·jnll.'1t�i hod11oty rl'lati,·ni rlC'lk_v a rr-latinti hlu11bk_,. pr-i 1;. Ohr. danl·111 podjt.�zi. Ti·mto 1H·jm<·11Mm hodn11t;l111 odpo,·id,i rlt j\·(·1;..f dPfnrrrntc·t· dna. t. j. rH'jn:·t :=ii l·rn:.:i,·ni :.:ila . . · "l'Khi · do podjt·ii 17.1.' mit ! ' : h l ·:..., llZ . l ·.1- . Prti pl ,•1md a'l. \' ffl f .'Z. tC.' . , \l" I ku--t • ,lt;•lk,· 11-1'\II lh·drnuli,·k\'·111 zatfi.,·nirn II. 111 lzL· snacl110 sc· n·hnot t 1 rd1111,·11l t · · pro1.atin1nt• zn tt,. i.P I iru. 7.,·pri: •du;.,u·· prutuky j:.:011 po11.�t(·ny :.:H:jru,rn(·r:n(· ph·:.: · · · ·,"·nla . i 1ln(· h, , , l,11, l' .. .. \·\ 1 • · :l. \l('tl·lllOll u:--t1 "1.on :--111,·idln lll'li pod :.:t11,·idly ,-�·c-h tri poll. .It_.n·lrni zi-c-j· I II r ,In " '''1 111<• h p1. 1k Jsou tl·odJC''/. l l'·lk l pro U('IJ1J10\l I II U\I I )� 1 111l·l11 dc·,·a:.:tuji ci l1l'inl•k nu dno 7.11 pndjl·zim. jczi tyto: = min · .t - 1 ) l.1.t· 1t:ch· 117..l-l\· f-it i: - ,' __ (.-1 - ll - 11 1; !1 1 ( H l' 1. 1 · 11 (• 11 P ). 1 �_!!_ I) !11 I . K 1. ,J ,·. I ',, ,I j i j11 11v It_\· H!'\t i II1. a j I c··· 11 = ,,.,�, (.I pt· <· It a r a k t <· r i :- t, \ ;i p d k I a d l· r a - TytM. vzorce vsak pro nadd v Huainci by daly ina m,i ; re- . d ,• , m II v e l i o bm1n = 1·5 . 1!°4 ·80 m + fj . 1 ·25 m = 44·70 m on Inl t e o r i e. rel 11 t, v ·� ( ti t , l u b k Y " Umnx = 2 . 2-1·80 m + 8. 1·2/i m = 5\HIO m. "tiv n i v,e I I k o t in y t ". o i· ' l ky. • 0;o v o·l i c ' Tyto delky jc srovnati s n11sf delkou pro Husincc £ = velikost1 dol :� rovn• a v a ni, 1 l1.1. d nu pr. o s · = L = J:,!lfl m • l· ednotn o 11 .,. �k,. . . ' · b 1. p cc11c, , 1 1 · · . . pod1 c •. • J ., c Jl' IC to kter6• ' n sovano. i· 6. d m o m11 nip ulac11 i 2_ J O ,1 c o I_ n e . . n z e 11 pod le Z ) b 1 ,. 1 0 y bl1ve J C � � n 1 k o­ Pt· o poh 1.ll t i· v i, l v cl ho roz b, o r ll 1· YC o /O· l ·, uvedcne . l' n k jc 111ozn s t hlo11 bky 11 cl,c \ k_ _) · ' c\ lll t' II SO\, , "i\ 11 1 i P 10 i sr1odar1. 1c . 11 c - u r O ·1 ·t 1 , l 1 o , 1 0 cl e 7• 1 111 ah�. L 1 no_ z. a .1 I po 1 J· ozi• a tak. 10. Obr. 10. c d e,· n sto,·111 bylo zbytt' CI• IU� Obclrzime tedy nil podkladc ratio­ nclni teu1·ic rcseni bez11ec· ne a zaro­ vcn t1 spo1·ne. B. D'•jc-li sc vytok ,·ody pod st11vicllcm pod hladino11 clolni rndy, llltLze SC ..tati, ze paprsek vytekajici vocly ncpnda kc cln11 spacliste. nybrz oblo11kem nnhoru ,·ypja­ tym pfoj uclnl (Han< II ,nc-I 1 I pro dcl.ku pnr 1·J zi �Kfl'h. Rt'l1hock l\ll�) vzorl'<' I . \V .. Ill. _ . . 1 · .t /i I - h ft,1· l>mln � S ho- Umnx •• � Ii, -

Ohr.!!. Ohr. 11. . jl'7,i. ,.011 delkn pod nwm':. cc II·, o ,·om,u. = \·., . I-�- m = :21)·0 m.nl . T'_._ � •n · I·-\:;·• nl =.. t.,·O 12. . ''""" - -- .t· ·"' 1n · pro Spy- . uzitel:n0ll dclku V obr. 7 ,·icli.me, zc paprsek se zvedne clocela nacl h.la- _jc •) RrO4-Vll'l·:? Blll �si �-o.·, m s tcmito ci,ly ou, dclkn L = I · 10·2-I: n1 a re-"11:'"o, . � ihne,� Li II

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= 7. ktl'r�· m,i 1. 1111k by�t finn<,sti J/ :1- J .i H. Proud znli- clRl1iim = z,, ,. <'1 l 0 i\1-m je nucen ve svem 1. oml-n.� v (1hr. I< 111,i" pohliz st11vidl11 1.1111k b.)'Hl l'i11noati dinu dolni..�od. _ t_, � ; 80 tvoH dva vlry o vodorovntl J/ 1 ·7, t<•dv \"l'lmi nizk,\°• : wki\ jc· virl{·ti . da liiim be088hu, Vpad at1 dom, p .l,Q_ - ill o . v ­ � men n d nlm. V obr t! y post 11p11 proud. jl'l,oz 1.1111k11 j1·,ll· uh,vni. rrui jii. Z\'l11(•11y lltsi pod pa pr.-kem, pu\'rch. ktc·r.<· Rt· d. dy ohjt·\'11j,·. 1,li:i.i- li S<· pmud prn11rl11 kritickfmu (,·i,: olJr. 7 \'C· �, 11di1 n n,d11i111 skoku prn­ st(•m). l'ad,i-li pnprsc·k kC' dnu. 111ohcm t0ho l,yt 1 dn' 3pritiny: I. U11C1' prn,th·di 11c111,i 'l"'cific,ko11 nihu I t/m • u_yl,r:i.

•11,1. _ ., ,•: v 1111·11�1. J:!ylr, 11k1i1.,i110 " ,tudii--; o n,dnim skoku -:tnrl11tc111, _ , ,o 1. t· i-lJ >t· ·ific:k,1 nilut , m1C':':i vody n vzdw·h11 1 vni-id ,·ir nud .,. "' pupr:-:kt·111. 1nuz,. hj·ti 1.nu, 11(· ml'11;i;i11 t·Zli I t/111 . Ta m1(•1. hrlo 11k1izii11n, Zt· tHto , pt.'Cificki/J u i. nihn j(· lirn rnt·nSLC'im nit:n�i jt· rnira ph·vs·;l·ll1 l-im ,·(·tSi j� ZIIHk l,y:,.t i-i11- -� . . :.· no,1 i J/. Pon(·vHdi. pi·i dn11t'· di...,poi-,il·i . j1·z11 ru•rn11Zt·nu• 111it i ,· li­ ,·11 nn zrwk l,vMf·inno:--t i. po11Zijr1H· k 1om11. all\·dwrn · rlo,t,tli ,. nhr. ; a , " .,·kr<·slt·11i· pa pr,k.,· d, d11 k,· d1111 Ohr. 12. �111-uliHtl· dr11h1'· ok(llt10:--Ii: z1t11·11�irrtl'. ;i l(·:,;1 u,1l TJH za{•;it ku _, . ...� . -�- ..! podjn.i. 111ini ,· 1.d111i 11111t·I,· trnrc-111 podj,·zf. jak j,· 1111- · n,·- . . l'" ""'kem tC'lc· .po,- lj,•1.i , hoh·ji-i dr j, kr!'sk·n , ohr. !l II I 11. \" 11id1 jsn11 ohrazy 1 11·CJ11drni po­ pln11Je v1r. l poc l ll . t d IC' 1111.Si<:h poku�u Pupr:--ky , za11jut(• polozf' ,·yk11znv·ily pntrny. . · c ,·nrn pm 1 , ' >< l ll · t1t>ll\·h11j<'-li plnuu sin hi lit II l'f-ipad ,. ul,r. 9 a I IJ jc• mnolu·111 priz11i­ ") ik ' ·i z ot · r l'aprsek ; aJ rll'nui p�i -iny. nh�- n:'.·jNi pro 11am1ilui1d drrn z.a pralu·m rodjt·'-i 111·Z pHpud · 81l' 11� •�p cifickc nih\' ' : > se v prostr ch J · ,- c1b . 7 n . tnki..t• ,. pNpadt· clani-m ohr. In i dla:i;lm ZH prahl·m pndjt 1. fmt1:i.1 · !,_\·1 i , ·y1u·dui11H. :!. Dr11lui."pi-iC·i11a. pro ktern11 pu pn..t•k rn11Zt.• pada1i pi-i ,·.\·tuk,1 pod vudo11 dr ,lu. jc· 11rl:--t rc•dini :-:ila , ktt•rii ,·z11ikH.. F1F. 13. �rran�cment oh.vlu·m pro11dn,·.\·,·h vl,ik,·n pf·i ,·.,··1nk11 pod �t11,· idlt•111. �mt·f·11jt· dlll11 kolrnn nu prc 11uloni ,·J;i krrn. L'rni�t i,JH·-li of the cac�bone of �,� -.ta,·idln. n·:--p. jt·lu1 do:--i·dnd I ni111. podlt· ohr. " . 0 · t. j. e oron bel-:11-- the ,:rate dill,· prot i ,odt· ud kr:ij<· :--pudii-itc·. ph·jim:i

� •trn,\·1111-.t i vo· �\ se t)ohyhuvnti hr't pndnl ke wrn. Tedy n1 z . doro,·ne. t\\ j

·du r. •11.-n.< A la )Jrofomfour py, et en do11111111t au ,degrti ,, de nqyage• Jes vallmrs de p -- n a p :r,,. Cette el811· Hifieation des JJheuomene• mdi9u;.s Jlll r Al et p et la "onstatatiou que la valeur (voi r l<•H fig. 14 et l!i) de cotg aP = 6 JJOUr toutes h•H valeur• d,• f,Pl d" 111, ain•i quo la det<'rmination empirique di' 111 vu eur /JJ -• out rPudu .J,ossi ble de doouire des equatiou• -- eo11<·0,r111111 t la lon­ ,cuo,ur {1• du rr,...a ut. 111 JJL•rte di' .. harge .lff,, duo au resHHlll eh·. - ,;tahl ies pour lo rOHH!l llt 1111;yi•, •t ui pWU1011t uux .�,,uutions rmur le rl'�!'luut 11011-noye <-11 y 1,oKant p I (\·oir IL>s <'

C''Hst 1mur,1 110i J'autt .. ur buse In t«�ori1• ratiom•Jlt;t • du luu,i,s in ,rn mortis"lfllllt llf sur It� 1,rirl<'iJJP!-1 !H1 in1nts: )

t. L'Pall"'o ..,·t· 1·011lu11t d'u11 bnrragP. pu r dt�vt•rsPment ou "'ous l 'ur, tp iuft'•ri1•ur,• d,• la \"HIIJU". 1111u1i fl'st,• ordinnirP- 1111•11t uu r1�g-i1111• torr1•r1tur11x. II fu ut trausformPr <"e rt•i,riml' torr,•ut1w11x f'fl ri•,ci1111• fluviul ftrnr1t111ill,•J. pur 1111 ,._.,,a ut t1·,·xl1t111,..,,,111.. 11 t uoyi·. :!.. \f i11 q11t• ,•1• rf',..._aut St' produisP. ii f11 11 I q111• It• fowl ,I,• la t·nv,·tt•· tlu ba.-.si u tl'amortis.,t•111t•11t snit £1 la pro­ fond1•11r 1· u11 -d1•sso11s d u 11in•a u df' r,•au 11'a n1I ffig. I. !!. :1 1. P y, , .rJ 1 ( 1111, cc : · 2 - .·/ - II ° '"' y · (A -1) 0 ° 't i , -f }" f't,/,1 JJ l' O fo II dt• II rt• f ff'f' t j \ 1 du ha..;"'jHff :&JllOl'- colgcc - cotgocP -5 I M•_:,q��'--- ; A•� ; fj.;,..,1•1tlf'Jlt. ., ]I A :l. l.":1 ut,•11r rt•,·011111111111)1' c·o11111H• valP11 r-. ratioru•IJps du 11 j ,.; /_PA-l ( ) -Jtg;r{p(A-f) -2_/j dt•l,{rt'· /J df' unya�I' , ... 11..... df' ,, - r� j11-.q11"i1 ,, r:,. A-1)-2 ; I -Jy/ -J) ; h, ""./T . II .J 1'- J ,{p( o p•I � (A-J)' -1. Pnr 1•011s1·· 11111•11° t l'a11IP11 r ,·oU"41r11it pou r J;i profou­ /M ' _ 4 '- colg« /yTf (A-1)-,J;•4H ·ft� 0 P f, d1•11r t•fft•d i\1' ) d11 lia,-.ir1 t1·:1111ort i ..;-.1•rrw11t J,,..; forrnufp� "H_·Y,(T [' p'(A -IJIJ l2 1',11111 I ·:!-·�' f.·l --11 �-1f"li /J 1 f.-l -11 1 ··., 'I l'rua ,: J·;, . , (A -I I n·;-:, .111 f.A 1) J

1 A = I" I + ,.,: _1/-; = , I · ."l _,·,�- ' I -� H __!{___ .,j ::. 11 111 !l.'I , i .�,. T ,··taut Ju profo11d,•11r ell' !",•a u 11'11rnl I fig. I. :!. :I i. !,, fotul du h;i.;.-.in d'a111orti -...;,•m,•11t Jlf'llf f";. f 1'1' -.i!11,·, Oil

'1 L1· 111/•m" a11t,•11r: L,• ha�-.iu d'a111orti-.-.1•1111·11t d u liar !':tl{f' r,·,-.. . noir ...ur 11!1 affl11P11I d.- la \'Jt:1\·a pri•-. d,• ll11- -.i11t•e. Tra\·,a11x .-1 ,·t11d1•-. \"11 111 J!l:l-1. _,. ,·11ir :111,..;i:x, ·1,, ('11111.:ri•..; J11 l•·r11utio11:il d,• \";n· i,-:-a tiou Bri1x,•II,...._ l!t::.-, ; rapport d1· l ·a11t1•11r ;·1 la d,•11xii·111" 1•011111111- 11i1·:itio:1.

1.-, ,� au-det1sous du niveau du lit aetuel de la ri,·i�rc- nu au memo niveau. ou enfin au-au. •rlon 1011 ciT�Ull&llCL.,. si PU• � T

6. �:n l"O qui cont·erne lu longueur du ba�•in d'amorti•· Re1111•11t ii rout di�t i nl(tll'r longueur rl'elle L t•t Ion­ ir-u-c..u r erret•tin, L, le long de ln(lu1•lle 111 tra1u,rom111- tio11 du c.·our1utLtorre11tnt•11x au t•ournnt n.tr auquillc 14C roil en t•rfet. n1111s ,� ri-lf . I. �- � /,. l, - Lo longueur () tl1•pend dP du hnrr11gr, du · 111 form,• d ,,.l'l"!loir, de lo1 hnutcur ,It• ,·hargr 1,. Pt dr la chute /, . 7. L'nutour clHcrmino In longueur du hnssin d'uruor­ ti!-l!wtnPnt f'n n lution nvc...· In longul•urL, l du rei-1,p.aut 11011- uoy(' rr�JH't'tif, ulor"' , L, 11/ c:::: �11y (.1 - 3) 8. C'on111u• vul(•ur-4 du �Ol•fri(·ir�11t ,, l"null'Ur rPt.·onrnni.lP sur lu ba"'l' dt• s� l'Si�ni"'f...'t•llt•..; de ,, :otf� ju,qu"i1 " r1 L, 111111 :f 4 !J1 L-1 - '-"'"'' :r:1 !I• r..i - :1 1. 1 9. II ro ut di•tl'rminer 111 µroroncl.,ur c•t lu ,ongn,•ur effL l·ti,·e Liu ba"'·"'ind'umort i��t•mt•nt1 1m11r It.• dl•bit It• plu..:. rlangl'r<•ux. Le dt"bit )(' JIIH� dn111i('t�rPnxr"'t ordi11uin•mc11t cclui qui tlo1111P lu vuh.•ur d,\ 11u,u,·l llll'rll 111 plu,; J,Crurut,• ce <111i t•orrl'�po11tl ordi1111in•111l'11t i, lu Jllu,; irrn11dl' n1- leur dt• l'i11rlPx JI clP torrentuo..;itt!.. 10. Pa rt..·c qtw In lo11,r11t•r t• ffN· t h·t• e-1t plu-. l'0llrh' ll lH' In louguou r d 11 rt'"'"'H111 rtort� rl.'"'JHt,•.:"t.'l if 1 I,, = 11/ le t:ournut d'l u11 ..;ortnnt tlu hu, ..in tl'arnorti"'"'l.'ILWllt a <:-tu_·ore ,uu• ,· ih·"'"'t"' Lilli p,t phi.. Jrra11d,· qt1t• la vitt•,-.p fltn·iult• , .., l'Orn•..;poruh111t au t·ura,·ti•r,· du lit 11111urPI. ('·c-.. t 1>0urq11oi ii fn nt d,•,·it•r I,• ,·ourunt d\•ntr v,•r..; It-, -111rfHl"l' au moy,•n c1·u11 paru1u·t -.i111t• :·, l',•xtrl•111itt'· ,1'1-1,·al dt• In t·nv,•ttl'. ufi11 qu'il nt• pui,,1• 1,u.. nffouill,•r I,· fo11J ti,• la ri,·it•n• i111111l;dinh'rtll•rtl ,•11 avaltl,•,·i, ·· du hu-,,i11 d'arnor- 1i..;..;1•n11•11t. 8011-. I,• ,·011ru11t J't•uu th• n•tll' mnuii•r,•. u11 tourbillo11 i1 uxt• hori1..011111I l't nya11t It• -.t•u-. d,• rntn tion pft.,.., du fond v,·r, h• 1u-1rHpt•t ... ,. 1•rrul11it. tit• ..:orlt· qut• t'l.' to11rhillo11 l· roth· dot11·1•111t·11t I,• 111u1t•ri1•I du lit 1,l11.s loin du pnr;qwt t·I h• dl•po ..,• i111111t·diat1•111,•111 t'II H\·:d du µana11Pl. I>,· ._. •• fnit,, 011 vn1t q11t• I,• pu,·,, 1•11 u,·nl du pnrap1• t�"'t inutilt•. 11. l.'tt11tt•ur dn1111t au purapt•t tlu hu--,i11 d'amorti-....,• meut \lilt' fonnt• tout i, fail ,imp!,• : ii l",•t 1hlit ,•11 fon11,· df' :!. :� 011 -I mnn·h,-.. don la ha11tt•11r ,•,t d,·11:\ foi, 1•111 .. JH'titt• qtw In h1r�1·ur. (',•tt,· form,· tit• parap,·t ,uffi l'lltil•rt•111t•nt pour lu clt•,·i1-1tio11 du 1·011ra111 d"1•n11 1•t ,. ,·,t h• rl1!t• print·ipnl du 1n1rap,·1. l.'au1t•11r l 'nppltqu,• 1011 jour:-t> u,·l."t" tit•, rl·--11ltut, tri'.,.., ,nti-.fui�a111,. I.<• 1·nurn11 tl'f'au ...· ,,,·01ilu111 U'u11 harrag,• pur d,,, ,•r ""t'ltlt lll ou ,011..: la ,·a1111t• 11t1t·i11t It•, ,nlt•ur, ii,· .\I d,• :! i1 \lour It� gra11d-.l· ,arrni;,r,•, dt• � i, 1:1. Pn-1r 111 profo111h•11r du 111-.-.i11 cl'umorti-.l't'Illl'lll ),, ... ,·al,•ur-- du rt,•l(rP ti,• uorn,:,• µ dt• t":! i1 1 ·a -.0111 -.n1i-.fui..;.a11 I'... 1., .... , .....,11 ... ,·x,-<·t1t•·-- 1 1 par l'a111t·11r 1·01h·Pr1rn11t It• n•,-.au d'1•'(1 li1t11 ..,•111t•nt 1111, ,·nlt•11r..; d1· .\I tit• I i1 :'4 ,•t aux ,·ul,·ur.. d,• I H :! ·, c. 11 r f j ..; t' II I tf O II 1• ii .., U I j -. f ii I r 1 I O II ,� I',, :\ I � ,• :1 11 ,. ,. ti ,. la pra t i II u ,. h , 11 r ;1 11 I , •r u ,.

It\

17 ·----�

Dans lee certains C88, si l'ecoulement de l'eau sous la vanne du ·bBJ!rage 88 fait au-d888ous du niveau de l'eau d'aval le eourant d'eau dl-passe, arque en bout, IE> radier. L'auteur a constate ce phenomime en realite pour l'eeoulement sous la vanne du barrage it Symburk sur l'Elbe (fig. IL 12). An ssi les e880iR s nr h• modi-le reduit pour le barrage a lllubokli sur la rivierr dr Vltava ont montre le meme phenomene (fig. 7, 81. llans 1•e cas la longueur eff1-.,tive I. , rln bassin d'amorti"�"rnent se ra('('ourci et l'effien,•ltl- du radier se r,;duit b,•nu .. onp. Le <'Durant d'eau jnillisMBnt sous la ,·nnne au-dessous du niveau d'aval se meut dans un miliru du mllme poids spl-cifiqne. AlorR ii doit se mouvoir 1mr l'inertio bori­ zontaleuumt mais ii <'hoiRil la voit• dP lo moindre rl-si­ sta11t>I'. Si on fnit la form,• du radh•r ,l'iipres lu .fig. 9. 10, le degr,• de novage imm.:-dinll'llll'nt ,•n nvol du Rl'l1il du barragep ,,,.1 tr� p,•tit, It• m,•lnuge elf'l' t•nn et cle l'nir 11 le 1micls s ''"· ifh1ut• plus 11etit ,,m• 1 kgldm'. ,•t 1>11r 1•011�,··q nt'Ucl' \r 1•ourn11t d'euu B'\"Rnt h• poidA BJn�t•i fiquo I kg;dm' tombe \'l'l'H le fond de ia ,•u,· ..t t,•. On 1n•ut aussi <'t·lair,·ir eel effet de la fai:on qu,• lo grande vite••e du ,·ouraut de l'enn jnilli••nnt MOUR In ,·1111111• l'nle,·,• (suee) In pt •lite qunntiti• de l'Pnu qui s,• troll\'P 1111 1•omme11l'P­ ment uu-J ,.,.011•.. du <'Olli-ant jailliMant dt• Rortl' qu'wll' Rous-J>rt.� siou !ifiP 1,roduit l't le 1•ournnt dr 1"t•1u1 t�t uttiri• ,·e.-.. It• fond. II •uffit IIOllr ntteindrl' J,. m;.mr .. rrrt ,h• donner au �Puil tin hnrra,rP la fornw indit111t;P J)nr rnuh•ur dn.ns In fig. 1:1. llnn!'-i 1••l eaM Ju longtu-nr t•frp1•th·t.l I., �.. pro­ long,• t'I l't'ffit-n<'ilt• dn r111lier IIIIIWll'III<'.